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?

EXPERT ANSWER

1) Solution: optimal solution : 10,560

Working:

	Standard Model (x)	Deluxe Model (y)	Maximum Total Profits
No of Bags	300	420	10,560
Profit ($) / Bag	10	18
Constraints			Total Hours of Prod. Used		Total Hours of Prod. Available	Slack Time
Cutting and Dyeing	0.7	1	630	≤	630	0
Sewing	0.5	0.833	500	≤	600	100
Finishing	1	0.667	580	≤	708	128
Inspection and Packaging	0.1	0.25	135	≤	135	0

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 Bags	708	0	14,160
Profit ($) / Bag	20	9
Constraints			Total Hours of Prod. Used		Total Hours of Prod. Available	Slack Time
Cutting and Dyeing	0.7	1	495.6	≤	630	134.4
Sewing	0.5	0.833	354	≤	600	246
Finishing	1	0.667	708	≤	708	0
Inspection and Packaging	0.1	0.25	70.8	≤	135	64.2

3) Solution: Optimal solution : 7,668

Working:

	Standard Model (x)	Deluxe Model (y)	Maximum Total Profits
No of Bags	540	252	7,668
Profit ($) / Bag	10	9
Constraints			Total Hours of Prod. Used		Total Hours of Prod. Available	Slack Time
Cutting and Dyeing	0.7	1	630	≤	630	0
Sewing	0.5	0.833	480	≤	750	270
Finishing	1	0.667	708	≤	708	0
Inspection and Packaging	0.1	0.25	117	≤	135	18