Enter the following LP into TORA and select the graphic solution mode to reveal the LP graphic screen. Next, on a sheet of paper, graph and scale the x1 and x2 axes for the problem (you may also click Print Graph on the top of the right window to obtain a ready-to-use scaled sheet). SOLUTION IN LINEAR PROGRAMMING and seek to find out as to how the graphical method of solution be used to generate optimal solution to a Linear Programming problem. Once the Linear programming model has been formulated on the basis of the given objective & the associated constraint functions, the next step is to solve.

Linear Programming Graphic Tutorial

Linear Programming (LP) affords the teacher a simple yet powerful way to demonstrate applications of constrained optimization. As such, it can be an effective pedagogical and demonstration tool in Intermediate Microeconomic Theory and other upper-division courses. Often an introduction to LP is included in a Managerial Economics course, Quantitative Methods course or in Operations Management.

As they learn LP, students may miss the fundamental economics principles by concentrating on demystifying the mathematics. Many textbooks stress geometric expositions using two variables and static graphics. Because even the simplest LP problem can result in a fairly complex set of static graphics, adapting the exposition to an animated step-by-step Flash™ presentation renders major improvements in pedagogical technique.

This tutorial solves a simple problem by breaking it into separate step-by-step parts that students can assimilate and review at their own pace. After a brief introduction to constrained optimization and the demonstration problem, the first two parts of the tutorial separately develop the objective function and the feasible (constraint) area through a combination of simple algebra and animated geometric expositions. In the third part, the objective function line is superimposed over the feasible space and shifted to arrive at the optimization solution. The last part of the tutorial demonstrates a few applications of sensitivity analysis.

The tutorial should be viewed many times for different purposes. Introducing students to LP may be best accomplished initially by concentrating solely on the overall geometric exposition. After the students grasp the basic idea of the process, they should learn how the algebraic specification of the problem is integrally tied to the geometric exposition. Finally, they should acquaint themselves with the terminology and nuances of LP including the concept of slacks, and “Sensitivity Analysis.”

After students use the first parts of the tutorial, (through the derivation of the constrained optimum), it may be instructive to build and solve some LPs on the computer. I have used Excel or Excel with the “What’s Best” add-in. The computer solution data include the optimum, slacks, and finally, dual values, the interpretation of which is addressed in the final “Sensitivity Analysis” section of this tutorial.

The problem used for this demonstration is typical of those found in Managerial Economics texts and is a slightly modified version of a example or problem from an early edition of Brigham & Pappas's Managerial Economics.

CONTINUE TO TUTORIAL

(Viewing this tutorial requires that your web browser has the Macromedia Flash™ plug-in installed. Most browsers have it installed, but if yours does not, follow this link to obtain (free) and install the plug-in: Macromedia Flash Player.)

Graphic Lp Optimizer Pro

Graphic Lp Optimizer Online

Description	Type	OS	Version	Date
Intel® Graphics - BETA Windows® 10 DCH Drivers This download installs the Intel® Graphics Beta Driver for Xe Dedicated, 6th - 11th generation, Apollo Lake, Gemini Lake, Amber Lake, Whiskey Lake, Comet Lake, Lakefield, Jasper Lake, and Rocket Lake.	Driver	Windows 10, 64-bit*	27.20.100.9616 Latest	5/26/2021
Intel® Graphics - Windows® 10 DCH Drivers This download installs the Intel® Graphics Driver for Xe Dedicated, 6th - 11th generation, Apollo Lake, Gemini Lake, Amber Lake, Whiskey Lake, Comet Lake, Lakefield, Jasper Lake, and Rocket Lake	Driver	Windows 10, 64-bit*	27.20.100.9466 Latest	5/14/2021
Intel® Graphics Driver for Windows 7/8.1 [15.36] This download installs the Intel® Graphics Driver for 4th Gen.	Driver	Windows 8.1, 32-bit* Windows 8.1, 64-bit* Windows 7, 32-bit* Windows 7, 64-bit*	15.36.41.5180 Latest	4/14/2021
Intel® Graphics Driver for Windows* [15.40] This download installs the Intel® Graphics Driver for Braswell, 4th and 5th generations.	Driver	Windows 10, 32-bit* Windows 10, 64-bit* Windows 8.1, 32-bit* 3 more	15.40.48.5171 Latest	2/5/2021
Intel® Graphics Driver for Windows* [15.45] This download installs the Intel® Graphics Driver for 6th Gen on Windows 7* and Windows 8.1/10 64-bit.	Driver	Windows 10, 64-bit* Windows 8.1, 64-bit* Windows 7, 32-bit* Windows 7, 64-bit*	15.45.34.5174 Latest	2/5/2021
Intel® Graphics Driver for Windows* [15.33] This download installs the Intel® Graphics Driver for Baytrail and 3rd generation.	Driver	Windows 10, 32-bit* Windows 10, 64-bit* Windows 8.1, 32-bit* 3 more	15.33.53.5161 Latest	10/23/2020
Radeon™ RX Vega M Graphics This download installs the Radeon™ RX Vega M 18.12.2 Graphics Driver for 8th generation.	Driver	Windows 10, 64-bit*	25.20.15002.58 Latest	1/10/2019
Beta Intel® Graphics Driver for Windows® 10 and Windows 7/8.1 [15.40] This download installs the Beta Intel® Graphics Driver for 4th and 5th generation. (15.40.26.4474)	Driver	Windows 10, 32-bit* Windows 10, 64-bit* Windows 8.1, 32-bit* 3 more	15.40.26.4474 Latest	6/24/2016
Intel® Embedded Media and Graphics Driver for Windows* Embedded Compact 2013 (build# 3070) v36.18.4: Install Package Install Package: Intel® Embedded Media and Graphics Driver (build# 3070) v36.18.4 MR4 (maintenance release 4) for Windows* Embedded Compact 2013.	Driver	Windows CE*	v36.18.4 Latest	2/26/2016
Intel® Graphics Driver for Windows® 7 & 8.1* [15.40 6th Gen] This download installs the Intel® Graphics Driver for 6th Gen.	Driver	Windows 10, 64-bit* Windows 8.1, 64-bit* Windows 7, 32-bit* Windows 7, 64-bit*	15.40.14.4352 Latest	12/23/2015
Intel® Graphics Driver for Windows® 10 [15.40][4th Gen] This download installs version 15.40.7.64.4279 of the Intel® Graphics Driver for Windows® 10, 64-bit.	Driver	Windows 10, 64-bit*	15.40.7.64.4279 Latest	9/1/2015
Intel® HD Graphics Production Driver for Windows® 10, 64-bit* (N-Series) This download installs the Intel® Graphics Driver for Braswell.	Driver	Windows 10, 64-bit*	15.40.1.64.4256 Latest	7/29/2015
Intel® Graphics Driver for Windows* [15.28] EOL This package installs the Intel® HD Graphics Driver version 15.28.24.4229 (9.17.10.4229) for Windows 7, Windows 8, and Windows 8.1*	Driver