Posted on by Judy

PLEASE TYPE IN A WORD DOCUMENT FORMAT AND SHOW STEP-BY-STEP EXCEL FORMULA!!! 13-7. Klein Industries manufactures three types of portable air compressors: small, medium, and large, which have unit profits of $20.50, $34.00, and $42.00, respectively. The projected monthly sales are: Small Medium Large Minimum 14,000 6,200 2,600 Maximum 21,000 12,500 4,200 The production process consists of three primary activities: bending and forming, welding, and painting. The amount of time in minutes needed to process each product in each department is shown below: Small Medium Large Available Time Bending/forming 0.4 0.7 0.8 23,400 Welding 0.6 1.0 1.2 23,400 Painting 1.4 2.6 3.1 46,800 How many of each type of air compressor should the company produce to maximize profit? a.Formulate and solve a linear optimization model using the auxiliary variable cells method and write a short memo to the production manager explaining the sensitivity information. b.Solve the model without the auxiliary variables and explain the relationship between the reduced costs and the shadow prices found in part a.

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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