Share
Explore BrainMass

# Linear Programming Graphically

I am having difficulty solving a linear programming problem graphically. Can you do this on an Excel Spreadsheet? I have attempted to do it on my own (see below) with some trouble.

Let M = number of Everett Parkas
Let R = number of Colorado Parkas
Max 100M + 150R
s.t.
30 M + 20R < 7200 Cutting time
45 M + 15R < 7200 Sewing time
0.8 M - 0.2R > 0 % requirement

I am having some trouble formulating constraints such as the % requirement constraint. Can you proceed with a systematic step-by-step fashion with formulating these types of constraints such as:

M must be at least 20% of total production
M>0.2 (total production)
M>0.2 (M+R)
M>0.2M + 0.2R
0.8M - 0.2R> 0

Here is what I have attempted to do on my own...

R
500
Sewing
400
% requirement
300 Optimal Solution
(65.45,261.82)
200
Cutting
100 Profit = \$30,000

0 M
100 200 300 400

Please note that I know that the optimal solution is M = 65.45 and R = 261.82; the value of the solution is z = 100(65.45) + 150 (261.82) = \$45, 818. I know the situation as an on-going production process, the fractional values represent partially completed Parka products.