Question

Question 9 1 pts The Return of Detroit City: Enpar manufactures engine parts for Ford using steel as an input. Enpar operates two plants, one in Detroit, MI and one in Greenville, SC. The production functions for the two Enpar plants are: Detroit: Qu= 135p -0.25 S02 Greenville: QG= 4156 -0.5562 where Qp and QG are the outputs of engine parts (in units) from the Detroit and Greenville plants, respectively. Sp and SG are the amounts of steel for the two plants. The firm has 189 units of steel available. How much steel should be sent to Detroit? Enter as a value. ROUND TO THE NEAREST WHOLE NUMBER

Answer 1

To find the optimal values ,the marginal products of both functions need to be equated. This is shown in image below

8 = 1350 -0.25 5b 8G = 4156 - 0.5 So ² Marginal 28. product of D' would be - 13- 0.550 BSD Marginal product of G would be da = 41-SG SG It iu quen that Spt SG = 189 - SG = 189 - SD Marginal products should be equal I 13-01.550 = 41-SG. 13-05 SD = 41- (189-5D) 13-05SD = 41- 189 + SD 13-41 + 189 = 1.550 SD = 161 = 107.33 107 1.5 SD=107. Hence 107 units be sent to Detroit