Question

D Question 25 1 pts A company can use cotton to produce gloves, hats, and shirts. The profit on a pair of gloves(G) is $5, the profit on a hat(H) is $9, and the profit on a shirt(s) is $20. The items are produced according to the following production functions: G=36CG H=22CH-0.5CH2 S = 81C3-C 2 where Co. Ch, and Cs are the pounds of cotton. There are 120 pounds of cotton available. How many pounds of cotton should be used to make shirts (Cs)? Enter as a value.

Answer 1

Profit per unit of Gloves & 85 Total profit from gloves 25 G Profit per unit of Hat 289 Total profit from Hat 2 9H Profit per unit of shirt 2820 Total profit from Shirt 2 20s. Hence, to tal profit is TP 2 TPG + TPH + TP.3 2 5 G + 9H+ 2os. 25*36C6 +9(22CH-0.5C+2) + 200816,-) TP 2 180 C + 198C4 - 4.5 G + 16206-2007 Company will maximize TP, subjected to constraint CGTC HTC, 2120

By Lagrange, La TP + X[120-CG -CH-Cs] = 180 CG 119864 -4.509 + 162066 2003 + 1/120-CG-CG - CH) Now, First order condition for maximum 2) 180-120 1 2180 - when az 180, then do so » 198-9CH - 20 2) 198 - 1809CH 2) CH2 18 » 1620 - 40C - 180 20 2) Cs a 1440 -|Cs 736) - 40

We know, Ca + CH + C 2120 2) Ca +36 + 2 2 120 [ Patting value of CHAC] Co z 120 - 38 Therefore, according to question , (36 pounds] Cotton is required to make shists