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:

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 $10. The items are produced according to the following production functions: G = 36CG H = 23CH-0.5CH? S = 80C5-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 hatss (CH)? Enter as a value.

Answer 1

Page 1 SOL - Given that the poorit on o pair of Gloves (G) is = $5 poolit on a het (H) is . = $9 polarit on a shigh (s) is = $10 poolit per hat - Masinal productieily in shirt Marginal Fgoductivity in Gloves polop it peyi polos or gloves = Marginal productivity in Hot pororit per shift Marginal productivity in Gloves = dg dog = 36 Marginal productivity in Hat = dulich =g3-ch Marginal productivity in shirt - do des = 80-cs According to condition of 1a0 pounds of cotton avelloble 120+5 = (23-ch19 -(80-cs) 10 12S = (23 - ch) - (30-c 10 solving the equation las = 23-ch)9 = (80-cs)io 23-cb = 80-CS - 9XIO

page 2 1-388 = 93-ch = 80-CS we get 1.388=28-ch ch=83-10388 :. Ich = 21.612 | we get 1388 = 80-cs cs = 80 - 1.388 :: Cs = 78.612 cotton used to make Gloves = 120-91.612-78.61- = 190 - 21.612 – 78.612 - 19.776 :