Question

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: Qo - 20 5p -0.25 Sp? Greenville: QG - 60 SG-0.5562 where Qp and Q are the outputs of engine parts (in units) from the Detroit and Greenville plants, respectively. Sp and So are the amounts of steel for the two plants. The firm has 160 units of steel available. How much steel should be sent to Greenville? Enter as a value.

Answer 1

ANSWER : To solve this,

We will use the concept of marginal productivity of steel at two plants.

Steel sent to Greenville = 80

marginal foo ducturity of steel at detroits flaut, MPO = e = 20-OSSO mengual foroducidiy # 134cu puscillo flaunts MPa = 60-88 . for optimal dietribution of steel MP = RP, 20-05-80 = 60-86 3 284–85 = 80 - CJ ..also we have $4+8=160 - ( ) adding equation (1) and (ic) , we get » SG=240 Wbulion d 186 = 80.

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