Question

1 pts Question 25 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 36CG H-23CH-0.5C2 S-80CS-Cs where 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 hats (CH)? Enter as a value.

Answer 1

Given that The profit ona paior of Gloves(6) is = $5 Profit on a hat CH) is =$9 profit on a shirt (s) is = $10 => Marginal productivity in Gloves profit pain of .. glove = margiral Productivity in = Hat Profit per hat = Marginal productivity in short profit pear shiut. => Maoriginal Productivity in Gloves = dG / deg = 36 >> Marginal productivity in Had a dh/dch = 23-ch => Marginal Productivity in shiot ads)dcs = 80-75 :. Accorating to condition of theor are S 120 pounds of cotton available. => 1205 = (a3-ch)q = (80-c5). las - (as-ch) 9 = (80-C5) 10

solving the equation os 195 = (a3-ch) q = (80-(s)10 las aute23-ch = 80-c5 910 - las = 1.388 9410 --> 1.388 = 23-ch = 80-25 => we get 1.388 = 23.ch ch = 23-1.388 (cha 21.612] We get 1.388 = 80-CS 09 - 80-1.388 es = 78.612) There are cotton available:120 pounds. cotton uyed to make gloves = 120-21-612-78-612 • 120-21.612 - 78:612 = 19.7766 30=