Question

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 $10. The items are produced according to the following production functions:G = 36CGH = 23CH - 0.5CH2S = 80CS - CS2where CG, 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 gloves (CG) ?Enter as a value.

Answer 1

Answer 1 Maximize : t = Total Profit = 59 +9H+ IOS Subject to : CH + CG + Cs = 120 (1) Now Ipe54 +911 7 105 - Thy = 5(364) + 9 (23 C4 - 0.5ch) - t1018063 - Cod legrange is given by 2= 5(36) CG + 9/23 (4-80544) +10(8065-48) th(120-Ly-CH -co). first order Condition: Od 20 =) 180 = 2 =() - dá zo = 9(23-CH) = x (3) a2 = 0 => 10 (80-263) = 1 ∞ (4) ton a Cg ICH acs. from (2) and (3) we get 9 (23-CH) = 180 => CH=3 from 2) and (4) weget 10 (80-263) = h = 180 => Cs = 3) Hence Pulting this in o) we get CG + 3 + 31 = 120 Hence, GG È 86 w