Question

Problem 2. Solve the following LP.

MAX Z= 75.00 x1 + 58.00 x2 + 46.00 x3 + 62.00 x4 Subject to
4.00x1 + 3.50x2 + 4.60x3 + 3.90x4 <= 600.00 2.10x1 + 2.60x2 + 3.50x3 + 1.90x4 <=500.00 15.00x1 + 23.00x2 + 18.00 x3 + 25.00x4 <= 3600.00 8.00x1 + 12.60x2 +9.70x3 +10.50x4<= 1700.00 (1.00X1 + 1.00x2)/(1.00x1+1.00x2+1.00x3+1.00x4)>=0.60

Solve this problem using R or Excel.
What are the values of Z, x1,x2,x3,x4 and slacks or surplus, shadow prices.

Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values

Answer 1

One will have to transform the last constraint to linear form as follows:

(1.00x1 + 1.00x2) / (1.00x1+1.00x2+1.00x3+1.00x4) >= 0.60

or, (x1 + x2) >= 0.60*(x1 + x2 + x3 + x4)

or, -0.40x1 - 0.40x2 + 0.60x3 + 0.60x4 <= 0

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Input to Excel worksheet:

Solver inputs:

Answer er report (shows the value of Z, x1,x2,x3,x4 and slacks or surplus)

Sensitivity report (shows the ranges and the shadow prices)