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Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 21L0.8K0.2 Furthermore, the cost function for a facility is given by the function:C(L, K) = 200L + 400K Suppose the monthly production goal of this facility is to produce 17,000 items. In this problem, we will assume L represents units of labor invested and K represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor L = your answer is exactly 1 decimal place) Units of Capital K your answer is exactly 1 decimal place) = (Show The minimal cost to produce 17,000 units is $ (Show Also, what is the minimal cost to produce 17,000 units? (Use your rounded values for L and K from above to answer this question.)

Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 21L0.8K0.2 Furthermore, the cost function for a facility is given by the function:C(L, K) = 200L + 400K Suppose the monthly production goal of this facility is to produce 17,000 items. In this problem, we will assume L represents units of labor invested and K represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor L = your answer is exactly 1 decimal place) Units of Capital K your answer is exactly 1 decimal place) = (Show The minimal cost to produce 17,000 units is $ (Show Also, what is the minimal cost to produce 17,000 units? (Use your rounded values for L and K from above to answer this question.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 21L0.8K0.2 Furthermore, the cost function for a facility is given by the function:C(L, K) = 200L + 400K Suppose the monthly production goal of this facility is to produce 17,000 items. In this problem, we will assume L represents units of labor invested and K represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor L = your answer is exactly 1 decimal place) Units of Capital K = your answer is exactly 1 decimal place) (Show (Show Also, what is the minimal cost to produce 17,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 17,000 units is $
Transcribed Image Text:Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 21L0.8K0.2 Furthermore, the cost function for a facility is given by the function:C(L, K) = 200L + 400K Suppose the monthly production goal of this facility is to produce 17,000 items. In this problem, we will assume L represents units of labor invested and K represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor L = your answer is exactly 1 decimal place) Units of Capital K = your answer is exactly 1 decimal place) (Show (Show Also, what is the minimal cost to produce 17,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 17,000 units is $
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