A companies has invested $ 1 million in the purchase of new machinery in its plant and does not intend to incur major capital expenditure over the next two years. The companies can manufacture a product according to the annual production function: \ (Q (L) = 30L-L ^ 2 \) , while the annual labor costs (in $ 000's) of are given by the function \ (C (L (L ) = 4L ^ 2 + 20L \) . The companies sells the product at $ 10,000 per unit. a) Determine the optimal level of production and labor in order to maximize profits. b) Find annual profits. c) Calculate the present value of the net profit achieved during 2 years of production assuming an interest rate of 5%.
A companies has invested $ 1 million in the purchase of new machinery in its plant and does not intend to incur major capital expenditure over the next two years. The companies can manufacture a product according to the annual production function: \ (Q (L) = 30L-L ^ 2 \) , while the annual labor costs (in $ 000's) of are given by the function \ (C (L (L ) = 4L ^ 2 + 20L \) . The companies sells the product at $ 10,000 per unit. a) Determine the optimal level of production and labor in order to maximize profits. b) Find annual profits. c) Calculate the present value of the net profit achieved during 2 years of production assuming an interest rate of 5%.
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter3: Benefits, Costs, And Decisions
Section: Chapter Questions
Problem 8MC
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A companies has invested $ 1 million in the purchase of new machinery in its plant and does not intend to incur major capital expenditure over the next two years. The companies can manufacture a product according to the annual production function: \ (Q (L) = 30L-L ^ 2 \) , while the annual labor costs (in $ 000's) of are given by the function \ (C (L (L ) = 4L ^ 2 + 20L \) . The companies sells the product at $ 10,000 per unit.
a) Determine the optimal level of production and labor in order to maximize profits.
b) Find annual profits.
c) Calculate the present value of the net profit achieved during 2 years of production assuming an interest rate of 5%.
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