Linear Programming Graphically
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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.
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The following posting helps solve a linear programming problem graphically.
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I use the standard setup of linear programming and show the objective function and constraints in the ...
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