Suppose that Par’s management (Problem 14) encounters the following situations: a. The accounting department evises its estimate of the profit contribution for the deluxe bag to $18 per bag b. A new low-cost material is available for the standard bag, and the profit contribution c. New sewing equipment is available that would increase the sewing operation capac- If each of these situations is encountered separately, what is the optimal solution and the per standard bag can be increased to $20 per bag. (Assume that the profit contribution of the deluxe bag is the original $9 value.) ity to 750 hours. (Assume that 10A +9B is the appropriate objective function.) total profit contribution?

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1) Solution: optimal solution : 10,560

Working:

Standard Model (x)Deluxe Model (y)Maximum Total Profits
No of Bags30042010,560
Profit ($) / Bag1018
ConstraintsTotal Hours of Prod. UsedTotal Hours of Prod. AvailableSlack Time
Cutting and Dyeing0.716306300
Sewing0.50.833500600100
Finishing10.667580708128
Inspection and Packaging0.10.251351350

Thus the optimal solution will be x = 300, y = 420 and the total profit contribution equals 10560 (= 10(300)+18(420) = 10560)

2) Solution: Optimal solution : 14,160

Working:

Standard Model (x)Deluxe Model (y)Maximum Total Profits
No of Bags708014,160
Profit ($) / Bag209
ConstraintsTotal Hours of Prod. UsedTotal Hours of Prod. AvailableSlack Time
Cutting and Dyeing0.71495.6630134.4
Sewing0.50.833354600246
Finishing10.6677087080
Inspection and Packaging0.10.2570.813564.2

3) Solution: Optimal solution : 7,668

Working:

Standard Model (x)Deluxe Model (y)Maximum Total Profits
No of Bags5402527,668
Profit ($) / Bag109
ConstraintsTotal Hours of Prod. UsedTotal Hours of Prod. AvailableSlack Time
Cutting and Dyeing0.716306300
Sewing0.50.833480750270
Finishing10.6677087080
Inspection and Packaging0.10.2511713518