1210daily: Problem 5 Previous Problem List Next (1 point) A company operates two
ID: 1123778 • Letter: 1
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1210daily: Problem 5 Previous Problem List Next (1 point) A company operates two plants which manufacture the same item and whose total cost functions are where q1 and q2 are the quantities produced by each plant. The total quantity demanded, q = qi + q2 , is related to the price, p , by How much should each plant produce in order to maximize the company's profit? G = 8.5 + 0.01q' and G-3.6 + 0.0393. p 70-0.03q. Y2 = Adapted from M. Rosser, Basic Mathematics for Economists, p. 318 (New York: Routledge, 1993)Explanation / Answer
Profit = Total revenue - Total cost
Total revenue = p x q = (70 - 0.03(q1 + q2)) x (q1 + q2)
Total cost = 8.5 + 0.01q12 + 3.6 + 0.03q22
Total profit (P) = (70 - 0.03(q1 + q2)) x (q1 + q2) - 8.5 - 0.01q12 - 3.6 - 0.03q22
Profit would be maximized when dP/dq1 = dP/dq2 = 0
70 - 0.06q1 - 0.06q2 - 0.02q1 = 0
70 - 0.06q2 - 0.06q1 - 0.06q2 = 00.
Solve for q1 and q2 :
q1 = 700 and q2 = 233.3
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