Available here are the following:---

- A sample paper for the MA3484 examination
- worked solutions for the sample paper

Also available are `lp_solve` input files, in
lp-format (the native lp_solve format) for
the Transportation Problem (Q1)
and
the Simplex Method Problem (Q3), together with
output from the Transportation Problem (Q1)
and
output from the Simplex Method Problem (Q3).

In using the
simplex method calculator
provided by `www.easycalculation.com` to
find the optimal solution to Question 3, the data

p = - 3 x1 - 2 x2 - 5 x3 - 9 x4 - 4 x5

was entered into the 'Maximize' box, and the data

9 x1 + 3 x2 + 5 x3 + 2 x4 + x5 = 14

2 x1 + 7 x2 + 3 x3 + 4 x4 + 3 x5 = 26

4 x1 + 2 x2 + 3 x3 + 6 x4 + 2 x5 = 13

was entered into the 'Subject to' box.

In using the
Simplex Method Tool
provided by `www.zweigmedia.com` to
find the optimal solution to Question 1, the data

Minimize p = 6 x11 + 8 x12 + 9 x13 + 6 x14

+ 5 x21 + 10 x22 + 3 x23 + 7 x24

+ 3 x31 + 9 x32 + 2 x33 + 4 x34

subject to x11 + x12 + x13 + x14 = 7,

x21 + x22 + x23 + x24 = 10, x31 + x32 + x33 + x34 = 13,

x11 + x21 + x31 = 5, x12 + x22 + x32 = 10,

x13 + x23 + x33 = 9, x14 + x24 + x34 = 6

was entered into the relevant box. The following solution was obtained:---

Optimal Solution: p = 150; x11 = 0, x12 = 7, x13 = 0, x14 = 0,

x21 = 0, x22 = 1, x23 = 9, x24 = 0, x31 = 5, x32 = 2, x33 = 0, x34 = 6

Similarly, to find the optimal solution to Question 1, the data

Minimize p = 3 x1 + 2 x2 + 5 x3 + 9 x4 + 4 x5 subject to

9 x1 + 3 x2 + 5 x3 + 2 x4 + x5 = 14,

2 x1 + 7 x2 + 3 x3 + 4 x4 + 3 x5 = 26,

4 x1 + 2 x2 + 3 x3 + 6 x4 + 2 x5 = 13

was entered into the relevant box. The following solution was obtained:---

Optimal Solution: p = 4171/270; x1 = 43/135, x2 = 418/135,

x3 = 0, x4 = 83/90, x5 = 0

Solutions to linear programming problems can be checked at the webpage https://www.easycalculation.com/operations-research/simplex-method-calculator.php

Solutions to linear programming problems can also be checked at the webpage http://www.zweigmedia.com/RealWorld/simplex.html

A command-line program called `lp_solve` is installed on the
computer system of the School of Mathematics, TCD. One can specify
the objective function and constraints in an input file which can
be supplied as standard input. A reference guide can be found
online at the webpage
http://lpsolve.sourceforge.net/5.5/

Back to Module MA3484: Methods of Mathematical Economics

Back to D.R. Wilkins: Lecture Notes

Dr. David R. Wilkins, School of Mathematics, Trinity College Dublin.