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Cashier Check Printing Software

Our Cashier’s, Money Orders and other Official Check modules can help you: Lower your costs. Print your entire check with copies or offsetting credit ticket for 7 cents. Increase Security. No one can access the software without a proper user name and password. The software tracks exactly who prints what checks to whom. EzCheckPersonal Check Printing Software v.2.0.9. EzCheckPersonal is a personal check designing and check printing software for personal use. EzCheckPersonal saves your money on checks. EzCheckPersonal will work with blank 3 or 4 checks per computer check paper with 8-1/2' X 11' size. File Name:ezCheckPersonalSetup.msi. Cashier Check Printing Software. EzCheckPersonal Check Printing Software v.2.0.9. EzCheckPersonal is a personal check designing and check printing software for personal use. EzCheckPersonal saves your money on checks. EzCheckPersonal will work with blank 3 or 4 checks per computer check paper with 8-1/2' X 11' size. Versaink magnetic black ink (micr) for bank compliant check printing. All-in-one system: print, copy, scan. Super compact and lightweight (5.13lbs) Network ready: built-in wireless (802.11b/g/n) connectivity. Versacheck gold software download & check paper included - everything needed to print your own checks! IDAutomation CheckPrinting and Design Software allows users to easily design, create and print bank checks onto blank or pre-designed check stock. Run checks by linking to an external database such as Microsoft Access, Excel or a CSV text file as a data source for a text, create checks in incremental order and attach a authorized signature as a graphic image.

How To Print A Cashier's Check

How To Print Checks With Checksoft

Can You Print A Cashier's Check

Cashier's Check Printing Software Download

How To Print A Cashier's Check

ezCheckPersonal is a personal check designing and checkprinting software for personal use. ezCheckPersonal saves your money on checks. ezCheckPersonal will work with blank 3 or 4 checks per computer check paper with 8-1/2' X 11' size.

File Name:ezCheckPersonalSetup.msi

Author:halfpricesoft.com

License:Shareware ($29.00)

File Size:1.96 Mb

Runs on:Win2000, Win7 x32, Win7 x64, WinOther, WinServer, WinVista, WinVista x64, WinXP, Other

A checkprinting software that eliminates customers' need to purchase expensive pre-printed blank checks in order to print checks and check stubs. our software is QuickBooks compatible. Using our software you can do the following things: print check. ..

File Name:Check Printing Software

Author:OnlineCheckWriter.com LLC

License:Commercial ($4.99)

File Size:5 Kb

Runs on:Android, BlackBerry, Handheld, Mobile Other, iPhone, iPod, iTouch, Java, Linux, Linux Console, Linux Gnome, Linux GPL, Linux Open Source, Mac OS X, Mac Other, MS-DOS, Netware, OpenVMS, Palm, Pocket PC, Symbian, Unix, Win2000, Win7 x32, Win7 x64, Win98, WinMobile, WinOther, WinServer, WinVista, WinVista x64, WinXP, Other, Not Applicable

IDAutomation Check Printing and Design Software allows users to easily design, create and print bank checks onto blank or pre-designed check stock. This product is free to use with the purchase of the MICR E-13B Font Advantage Package which is located at: http://www.idautomation.

File Name:IDAutomation_MICR_Check_Design_Application.zip

Author:IDAutomation.com, Inc.

License:Freeware (Free)

File Size:741 Kb

Runs on:WinOther, Win98, WinXP, Win7 x32, Win7 x64, Windows 8, Win2000, WinServer, WinVista, WinVista x64

MICR CheckPrinting module for Medlin Payroll and Medlin Accounts Payable. Author: Jerry Medlin - Shareware Hall of Fame - Recipient of the FIRST Shareware Industry Award for Best Business and Financial Software.

File Name:Medlin32.exe

Author:Medlin Accounting Software

License:Shareware ($48.00)

File Size:1.15 Mb

Runs on:Windows

CheckPrinting Software 2000 prints MICR checks for USA and Canadian banks from blank check stock and can also create pre-printed bank checks for accounting applications including Quicken, QuickBooks or Microsoft Money, and best of all it is FREE.

File Name:cps2000.exe

Author:CheckPrintingSoftware.com

License:Freeware (Free)

File Size:3.08 Mb

Runs on:Windows 95, 98, Me, NT

Easily design, create and print business bank checks with the IDAutomation MICR CheckPrinting Software. Features include WYSIWYG design screen, VB scripting, database connectivity, signature image and check number tracking. Includes security fonts. ..

File Name:IDAutomation_MICR_Check_Design_Application.zip

Author:IDAutomation.com, Inc.

License:Shareware ($139.00)

File Size:23.37 Mb

Runs on:WinXP, WinVista, WinVista x64, Win7 x32, Win7 x64

This program helps you to manage your customer information and prints check to your customers. If you need to print a lot of checks, you must try this software. This software stores your client information to a database. You can insert, delete,. ..

File Name:MemCheck.zip

Author:MemDB Technology Company

License:Shareware ($70.00)

File Size:1.39 Mb

Runs on:Win95, Win98, WinME, WinNT 4.x, WinXP, Windows2000

Print checks and their accompanying letter directly from your Mac with this easy to use checkprinting application : enter the order (payee), the Dollar amount, and voila ! Standard and wallet size checks supported (Versacheck 1000-3001).

File Name:CheckWriterIIITrial.dmg

Author:Match Software

License:Shareware ($19.99)

File Size:44.89 Mb

Runs on:Mac OS X

Print checks and their accompanying letter directly from your PC with this easy to use checkprinting application : enter the order (payee), the Dollar amount, and voila ! Standard and wallet size checks supported (Versacheck 1000-3001, Quickbooks).

File Name:CheckWriterIIITrial.zip

Author:Match Software

License:Shareware ($24.99)

File Size:65.77 Mb

Runs on:Win2000, WinXP, Win7 x32, Win7 x64, Windows 8, Windows 10, WinServer, WinOther, WinVista, WinVista x64

File Name:CheckWriterIIITrial.dmg

Author:Match Software

License:Shareware ($19.99)

File Size:44.89 Mb

Runs on:Mac OS X

Onlinecheckwriter.com is a Cloud based CheckPrinting Software, which is one of the best Check writing software available in Market using by many leading companies, organizations, government agencies, Many Non Profit Organizations. ..

File Name:Check Writing Software

Author:Online Check Writer

License:Commercial ($4.99)

File Size:5 Kb

Print checks directly from your PC with this easy to use checkprinting application : enter the order (payee), the Dollar amount, and voila ! Groove agent 4 tutorial. Standard and wallet size checks supported (Versacheck 1000-3001, Quickbooks). Print deposit slips.

File Name:CheckPrintRTrial.zip

Author:Match Software

License:Shareware ($19.99)

File Size:69.9 Mb

Runs on:Win2000, WinXP, Win7 x32, Win7 x64, Windows 8, Windows 10, WinServer, WinOther, WinVista, WinVista x64

How To Print Checks With Checksoft

Cashier Check Printing - Cashier Check - Ez Check Printing - Check Printing Access - Check Printing Template

Can You Print A Cashier's Check

Cashier's Check Printing Software Download

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estloading674 · 3 years ago

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Watchdogs

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Groove Agent 4

Groove Agent 4 includes a very well-specified pattern editor. Amongst the other options here is the Classify Slices feature. This will automatically attempt to place the slices into one of five basic classes — kick, snare, hi-hat, tom and percussion — and these then appear colour coded within the display. Groove Agent 4 is the ultimate drum studio and virtual drumming instrument for producers and songwriters working in any modern musical style. This unique instrument combines three specialist rhythm modules in one: craft dazzlingly authentic drum tracks, produce dancefloor-filling beats and design slinky percussive grooves with a dedicated Agent for each task; combine up to four Agents for a.

Groove Agent 4 Vs 5

Groove Agent 4 Manual

Groove Agent 4 Catalina

Groove Agent 4 Tutorial

Finally we have a fancy virtual version of a drum-oriented Swiss Army knife, a magic all-in-all pack that could cover your every drum need – impressive functionality for a surprisingly low price.

by Alex Arsov, Nov. 2014

We at SoundBytes always talk about the software that we are working on at the moment. When I mentioned in an email how satisfied I was with a Groove Agent 4, Suleiman, our drum expert, wrote me that he hadn’t tried it yet. But in going through the specifications, he noticed that it has only eight layers per pad. He thought this could not be enough, at least for such a good instrument, as I claimed that Groove Agent 4 was.

More or less, this is the main story about Groove Agent 4. You can find better-equipped or more highly-specialized VST instrument for every particular section or function of Groove Agent 4 – e.g. Rayzon Jamstick mimicking behavior of a real drummer. Superior Drummer or Steven Slate Drums are a bit snappier when a rock kits start to groove. Fxpansion Geist has more advanced loop manipulation tools and so on. But all those tools cover just small specialized niche or function, all of which Groove Agent 4 has. Being a reviewer for so many years, you can imagine that I have all those specialized tools, but no matter. It happens that since I got Groove Agent 4, it has become my main tool for all percussion and drum tasks. It has proven to be the most complete drum workstation available at the moment, with a really big and versatile library, a great collection of MIDI grooves and an almost endless, deep collection of tools and controllers covering almost every aspect of drum manipulation and programming. It simply offers a great number of tools for working with drum loops, MIDI clips or separate hits and kits.

Groove Workstation

Groove Agent 4 Vs 5

Installation is pretty straightforward. Of course, as this is a Steinberg product, you must have a USB licenser. If you own Cubase, then you already have it; if not, you can buy it from Steinberg. The only minus is that installation program doesn’t ask you where to install the VST 2 version of the program, so I’ve spent a few days trying to figure how to make it work with other DAWs. After finding the VST 2 version and copying it to my common VST directory, it worked as it should.

I’m not familiar with any of the older versions, but even being a novice in Groove Agent series, it is not difficult to figure how to get started. There are two facts that you will notice after first few minutes of toying with Groove Agent 4. The first one is that the included kits and loops sound really good: crisp on the highs, clear and “attacky” in the mid-range and having a fine defined, punchy low end, all in all fitting perfectly in a mix. The second fact is that the whole workstation is outfitted with a massive selection of options. Thankfully everything is logically ordered, so you can go deeper and deeper from one window to another one without losing yourself. Groove Agent 4 is obsessively detailed. Looks like Steinberg locked a few programmers in a basement for a year and half, letting them out only if a Steinberg inquisition inspector squad couldn’t find any bad spots. (OK, I found one, Groove Agent 4 doesn’t support MIDI out, so you can’t record your MIDI manipulations in real time directly into sequencer – but as the previous version supported that, according to some forum posts, I presume this is just a temporary fault that might be corrected in next update.)

All in all, it is very impressive that Groove Agent 4 not only covers every drum manipulation aspect that we can find in the market in various third party plug-ins (loop manipulation with slicing, and auto-classifying hits based on a frequency range inside the imported loop, MIDI pattern editing, building kits, sample editing, programming a virtual drummer, mixing kits or even separate hits internally with a great arsenal of implemented effects, and so on … ), but it goes really deep in every named separate aspect, offering a great number of additional controllers and tools which add plenty of new sub-windows, allowing editing of details that are mostly expected from specialized plug-ins. Groove Agent 4 is a drum Swiss Army knife. You name it and Groove Agent 4 will frame it.

Bible in Details

Groove Agent 4 allows us to load up to four different engines, or different kits or loops at once. Actually, it is four-channel multi-timbral, as we used to say in the old sampler days. That means that you can have a real drum kit with additional MIDI pattern on the first channel, percussions along with MIDI patterns that come with specific preset on a second channel and two additional loops on other two channels – or even loop elements ranked over the pads ready to trigger them through a Rex-like MIDI clip that you can drag it on a track. You just need to press a slice button after you import your loop and it is done – of course, all four channels could be independently controlled through four different MIDI channels in your sequencer and all four channels can carry any combination of the described elements, so, you can have four different percussion presets or two acoustic along with two percussions and so on.

The whole Groove Agent 4 structure is divided into three essential parts, or agents as they call them. Acoustic agent brings three different acoustic kits: Studio, Rock and Retro Kit. There are 55 different presets, styles for those three kits with appropriate preprogramed MIDI clips, bringing intros, ends, separate elements of the rhythm and whole rhythm patterns. Second one is a Percussion Agent bringing a large number of various percussion instruments along with 125 different presets, styles and great number of MIDI pattern loops. The last one is a Beat agent with 102 different presets and great number of (as far as I know over 100) different kits for all sort of electro RnB Dance and all other “beat machine” styles along with even bigger number of MIDI grooves. All three Agents have over 3800 various MIDI patterns, being divided into loops, intros endings and separate loop elements. Not to mention that you can drag and drop your MIDI patterns from DAW directly to any of the 128 pads saving them as a Pattern group for further use for any other song or a kit.

Every agent brings different set of controllers specific to that agent. In Acoustic agent, the most specific controller is a XY controller allowing you to balance between two parameters; intensity and complexity. The first one determines how hard the hits will be played inside the MIDI pattern. The other, Complexity, determines the pattern, adding or taking away some elements to the MIDI pattern, like additional drum hits, more hats for a chorus. It differs from pattern to pattern according to the selected style. There are a nice number of styles that determine that behavior and can be implemented to any pattern. Most are predefined, but with a single click you can open style window for any pattern changing that style.

Each of the three agents also brings a large number of additional controllers that you can reach through hierarchically ranked editing buttons. I have been using Groove Agent 4 for almost a month, using it daily, but I’m still discovering more new things. I’m not so sure what developer manager had chewed during the developing phase but I presume it was something extra strong (no offense please) because I haven’t seen so complex instrument for a long, long time. Thankfully the whole structure is logical and straightforward. So you can easily start using this instrument, finding all basic elements without any trouble, but when you start digging a bit deeper … it is like exploring ancient catacombs or sitting in a Jumbo Jet’s cockpit.

All Together

At the main window we can see two buttons that determine editing field, dividing all further editing depending whether you chose the Instrument or Pattern section. That is common to all three agents, the first one, the Instrument section, is a place where you can fine tuning all kit elements using a set of basic parameters differing from agent to agent. Acoustic and Percussion agents have a set of ADSR controllers for most of the kit elements along with additional room, tune, bleed and overhead controller knobs for every kit element along with a few specific additional ones for hats, like a knob for controlling the bow, tip and edge level, while most of the percussion instruments contain only tune and room knobs along with attack, decay and release knobs. Of course there is also an additional MIDI FX section where you can set some additional MIDI controlling elements for some of the kit elements.

The Instrument section becomes far more complicated for a Beat agent, where the arsenal of tools goes much deeper for any selected sample (or loop) from the kit. The editing window has got seven additional sub-windows where you can fine tune any aspect of the selected hit. Main, pitch, filter, slice, amp, sample and MIDI FX sub-windows offer a great number of editing possibilities that go far beyond just basic tuning every kit element. It is also pretty straightforward to set layers for a single pad, if you import up to eight different samples to one of the sixteen pads, all samples will be automatically ranked over the velocity range from the first to the last one. Of course, one preset can contain up to eight pad windows, so it is possible to load up to 128 different samples (without counting layered sounds) in one kit.

In the Pattern section, the main feature, at least for me, is a Pattern editor, a drum MIDI-editing-like window, where you can edit selected pattern changing, adding or deleting some MIDI elements. This pattern editing window is common to all three agents. There are also few other editors that can be found inside Pattern section, where you can edit some other parameters, like defining the swing amount or adding, deleting or saving some other patterns.

More and More

On the right we have another four buttons where the Edit button opens a different window depending on whether we are in the Instrument or Pattern section, while other three are common, no matter which section we have selected. The Load button opens a small but mighty browser where you can load kits, changing pattern groups getting new interesting combinations or even browse through separate kit elements replacing just a snare or any other instrument. The Next button opens a Mixer window where you can add up to 29 different types of effects to any of the selected output – as Groove Agent 4 offers up to 16 channels – right click on a drum pad and you get an option to select output to that pad or to select different effects for to any of the used Agents. Regarding effects – don’t make me start naming them as there are almost more effects than you can find on average DAW, and every effect has additional parameters for fine tuning the processed sound. The last button opens Options window for optimizing some essential parameters, like selecting how much RAM should be reserved for kit use, an optional bit rate, and few similar general things.

Virtually Everything

We should not forget one function of a virtual drummer, one similar to something we could find on Jamstix. With this function you can trigger patterns with your MIDI keyboard, setting auto complexity of how often some randomizing elements should apply, a number of bars before one of the breaks will appear, level of quantization, swing level, when crash should appear and similar things. More or less, it works as it should. I miss ability here to record the end result as a MIDI file, doing some further editing, changing this and that. But as we mentioned in the first part of the article, I presume this feature should appear in some future update.

It Could Become an Endless Story

This is just a review, so we really can’t go through all details that are implemented in this comprehensive workstation. It is a fact that Groove Agent 4 offers far more than just an essential set of options and tools for all sort of drum manipulation, no matter if we are talking about live kits, percussion, rhythm machines or even drum samples or third party loops. In most cases you will not run out of editing capabilities no matter how much picky you are regarding the end result. For me, it is an ideal tool to achieve end results in a far less time than I’ve become accustomed to. At the moment, it is the most complete drum workstation on the market. The main advantage is not just the level of editing possibilities, but also ability to work with different tools or even approaches and techniques under the same roof, being able to combine them without constantly switching between different tracks and plug-ins. In times past, I wasn’t especially keen to use just one tool for all those tasks, as there was always the problem of mixing all those different elements. If they were in the same box, having insufficient control over the separate elements was the price paid. But as most of the included kits, patterns and presets are already optimized in advance …

Groove Agent 4 sounds so good and offers an almost endless number of options in its menus, assembling so much diverse functionality under the same roof, that you could easily forget some extra abilities that you can find in some other, more specialized instruments or plug-ins. Actually, you can’t believe what everything Steinberg squeezed inside that small window of a Groove Agent 4 considering it’s more than reasonable price of €179 EUR.

Afterparty

Groove Agent 4 Manual

Groove Agent 4 Catalina

At the time I’m writing this article, we already have gotten the first Groove Agent 4 extension. I presume there will be much more in a near future.

Until then, enjoy the first-class drum Babylonia, where thousands of different sounds sound like one drum pattern. Ladies and Gentleman (a short break with a drum roll at the end) – The Groove Agent 4!

More info on:

Groove Agent 4 Tutorial

You may also be interested in:

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Excel Solver Nt Generating Sensitivity Report

In my limited experience using Solver in Excel 2010 SP1, the Solver Results dialog box typically shows Sensitivity as an option when the Solving Method (selected in the Solver Parameters dialog box) is GRG Nonlinear or Simplex LP, and the Sensitivity option is not available when the Solving Method is Evolutionary. Hello all, I am trying to generate a sensitivity analysis based on a max cost of 10 but the sensitivity report is not showing after I run the solver. The sensitivity report would be needed to test the variables when I change the max cost.

Applications

Linear optimization can be applied to numerous fields, in business or economics situations, and also in solving engineering problems. It is useful in modeling diverse types of problems in planning, routing, scheduling, assignment and design (2).

Some examples of applications in different industries

Petroleum refineries

One of the early industrial applications of linear optimization has been made in the petroleum refineries. An oil refinery has a choice of buying crude oil from different sources with different compositions at different prices. It can manufacture different products, such as diesel fuel, gasoline and aviation fuel, in varying quantities. A mix of the purchased crude oil and the manufactured products is sought that gives the maximum profit.

Manufacturing firms

The sales of a firm often fluctuate, therefore a company has various options. It can either build up an inventory of the manufactured products to carry it through the period of peak sales, or to pay overtime rates to achieve higher production during periods of high demand. Linear optimization takes into account the various cost and loss factors and arrive at the most profitable production plan.

Food-processing industry

Linear optimization has been used to determine the optimal shipping plan for the distribution of a particular product from different manufacturing plants to various warehouses.

Telecommunications

The optimal routing of messages in a communication network and the routing of aircraft and ships can also be determined by linear optimization method.

J E Beasley

OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.

Linear programming - sensitivity analysis - using Solver

Recall the production planning problem concerned with four variants of the same product which we formulated before as an LP. To remind you of it we repeat below the problem and our formulation of it.

Production planning problem

A company manufactures four variants of the same product and in the final part of the manufacturing process there are assembly, polishing and packing operations. For each variant the time required for these operations is shown below (in minutes) as is the profit per unit sold.

Given the current state of the labour force the company estimate that, each year, they have 100000 minutes of assembly time, 50000 minutes of polishing time and 60000 minutes of packing time available. How many of each variant should the company make per year and what is the associated profit?

Suppose now that the company is free to decide how much time to devote to each of the three operations (assembly, polishing and packing) within the total allowable time of 210000 (= 100000 + 50000 + 60000) minutes. How many of each variant should the company make per year and what is the associated profit?

Production planning solution

Variables

Let:

xi be the number of units of variant i (i=1,2,3,4) made per year

Tass be the number of minutes used in assembly per year Tpol be the number of minutes used in polishing per year Tpac be the number of minutes used in packing per year

where xi >= 0 i=1,2,3,4 and Tass, Tpol, Tpac >= 0

Constraints

(a) operation time definition

Tass = 2x1 + 4x2 + 3x3 + 7x4 (assembly) Tpol = 3x1 + 2x2 + 3x3 + 4x4 (polish) Tpac = 2x1 + 3x2 + 2x3 + 5x4 (pack)

(b) operation time limits

The operation time limits depend upon the situation being considered. In the first situation, where the maximum time that can be spent on each operation is specified, we simply have:

Tass <= 100000 (assembly) Tpol <= 50000 (polish) Tpac <= 60000 (pack)

In the second situation, where the only limitation is on the total time spent on all operations, we simply have:

Tass + Tpol + Tpac <= 210000 (total time)

Objective

Presumably to maximise profit - hence we have

maximise 1.5x1 + 2.5x2 + 3.0x3 + 4.5x4

which gives us the complete formulation of the problem.

Solution - using Solver

Below we solve this LP with the Solver add-in that comes with Microsoft Excel.

If you click here you will be able to download an Excel spreadsheet called lp.xls that already has the LP we are considering set up.

Look at Sheet A in lp.xls and to use Solver do Tools and then Solver. In the version of Excel I am using (different versions of Excel have slightly different Solver formats) you will get the Solver model as below:

but where now we have highlighted (clicked on) two of the Reports available - Answer and Sensitivity. Click OK and you will find that two new sheets have been added to the spreadsheet - an Answer Report and a Sensitivity Report.

As these reports are indicative of the information that is commonly available when we solve a LP via a computer we shall deal with each of them in turn.

Answer Report

The answer report can be seen below:

This is the most self-explanatory report.

We can see that the optimal solution to the LP has value 58000 (£) and that Tass=82000, Tpol=50000, Tpac=60000, X1=0, X2=16000, X3=6000 and X4=0.

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Note that we had three constraints for total assembly, total polishing and total packing time in our LP. The assembly time constraint is declared to be 'Not Binding' whilst the other two constraints are declared to be 'Binding'. Constraints with a 'Slack' value of zero are said to be tight or binding in that they are satisfied with equality at the LP optimal. Constraints which are not tight are called loose or not binding.

Sensitivity Report

The sensitivity report can be seen below:

This sensitivity report provides us with information relating to:

changing the objective function coefficient for a variable

forcing a variable which is currently zero to be non-zero

changing the right-hand side of a constraint.

We deal with each of these in turn, and note here that the analysis presented below ONLY applies for a single change, if two or more things change then we effectively need to resolve the LP.

Changing the objective function coefficient for a variable

To illustrate this suppose we vary the coefficient of X2 in the objective function. How will the LP optimal solution change?

Currently X1=0, X2=16000, X3=6000 and X4=0. The current solution value for X2 of 16000 is in cell B3 and the current objective function coefficient for X2 is 2.5. The Allowable Increase/Decrease columns tell us that, provided the coefficient of X2 in the objective function lies between 2.5+2 = 4.5 and 2.5 - 0.142857143 = 2.3571 (to four decimal places), the values of the variables in the optimal LP solution will remain unchanged. Note though that the actual optimal solution value will change as the objective function coefficient of X2 is changing.

In terms of the original problem we are effectively saying that the decision to produce 16000 of variant 2 and 6000 of variant 3 remains optimal even if the profit per unit on variant 2 is not actually 2.5 (but lies in the range 2.3571 to 4.50). Similar conclusions can be drawn about X1, X3 and X4.

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Forcing a variable which is currently zero to be non-zero

For the variables, the Reduced Cost column gives us, for each variable which is currently zero (X1 and X4), an estimate of how much the objective function will change if we make (force) that variable to be non-zero. Note here that the value in the Reduced Cost column for a variable is often called the 'opportunity cost' for the variable.

Hence we have the table

where we ignore the sign of the reduced cost when constructing the above table. The objective function will always get worse (go down if we have a maximisation problem, go up if we have a minimisation problem) by at least this estimate. The larger A or B are the more inaccurate this estimate is of the exact change that would occur if we were to resolve the LP with the corresponding constraint for the new value of X1 or X4 added.

Note here than an alternative (and equally valid) interpretation of the reduced cost is the amount by which the objective function coefficient for a variable needs to change before that variable will become non-zero.

Hence for variable X1 the objective function needs to change by 1.5 (increase since we are maximising) before that variable becomes non-zero. In other words, referring back to our original situation, the profit per unit on variant 1 would need to increase by 1.5 before it would be profitable to produce any of variant 1. Similarly the profit per unit on variant 4 would need to increase by 0.2 before it would be profitable to produce any of variant 4.

Changing the right-hand side of a constraint

For each constraint the column headed Shadow Price tells us exactly how much the objective function will change if we change the right-hand side of the corresponding constraint within the limits given in the Allowable Increase/Decrease columns

Hence we can form the table

For example for the polish constraint, provided the right-hand side of that constraint remains between 50000 + 40000 =90000 and 50000 - 10000 = 40000 the objective function change will be exactly 0.80(change in right-hand side from 50000).

The direction of the change in the objective function (up or down) depends upon the direction of the change in the right-hand side of the constraint and the nature of the objective (maximise or minimise).

To decide whether the objective function will go up or down use:

constraint more (less) restrictive after change in right-hand side implies objective function worse (better)

if objective is maximise (minimise) then worse means down (up), better means up (down)

Hence

if you had an extra 100 hours to which operation would you assign it?

if you had to take 50 hours away from polishing or packing which one would you choose?

what would the new objective function value be in these two cases?

The value in the column headed Shadow Price for a constraint is often called the 'marginal value' or 'dual value' for that constraint.

Note that, as would seem logical, if the constraint is loose the shadow price is zero (as if the constraint is loose a small change in the right-hand side cannot alter the optimal solution).

Comments

Different LP packages have different formats for input/output but the same information as discussed above is still obtained.

You may have found the above confusing. Essentially the interpretation of LP output is something that comes with practice.

Much of the information obtainable (as discussed above) as a by-product of the solution of the LP problem can be useful to management in estimating the effect of changes (e.g. changes in costs, production capacities, etc) without going to the hassle/expense of resolving the LP.

This sensitivity information gives us a measure of how robust the solution is i.e. how sensitive it is to changes in input data.

Note here that, as mentioned above, the analysis given above relating to:

changing the objective function coefficient for a variable; and

forcing a variable which is currently zero to be non-zero; and

changing the right-hand side of a constraint

is only valid for a single change. If two (or more) changes are made the situation becomes more complex and it becomes advisable to resolve the LP.

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