a) Formulate LP
Decision variables: S, M, L be the quantity of Small, Medium and Large air compressors to produce
Objective: Max 20.5S + 34M + 42L
s.t.
S >= 14000
S = 6200
M = 2600
L = 0
b) Solution using Excel Solver follows:
https://media.cheggcdn.com/media%2F231%2F2316f974-d1d9-44ba-98cc-e538dfeb5644%2FphpZqnt9H.png
Formula:
E7 =SUMPRODUCT(B7:D7,$B$13:$D$13) copy to E7:E9, E11
Optimal solution:
Number of Small air compressors to produce (S) = 16157
Number of Medium air compressors to produce (M) = 6200
Number of Large air compressors to produce (L) = 2600
Optimal value (profit) = 651,221
Sensitivity report:
https://media.cheggcdn.com/media%2F6ba%2F6ba85537-69dc-419b-99fc-1ceb1805585e%2FphpHVuN63.png
Sensitivity report shows that painting is binding constraint.
Shadow price of painting is 14.64, which means that each additional time unit of painting operation yields an increase in total profit by 14.64, the maximum increase is limited to 6780
Shadow prices of Bending and Welding are 0, which means that additional capacity of these processes, will not lead to any increase in total profit.
Reduced costs indicate the quantum of improvement in the profit per unit, which will keep the optimal solution unchanged.
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