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Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 8L0.3 K0.7 Furthemore, the cost function for a facility is given by the function: C(L, K) = 500L + 100K Suppose the monthly production goal of this facility is to produce 9,000 items. In this problem, we will assume 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 = (Show your answer is exactly 1 decimal place) Units of Capital K = (Show your answer is exactly 1 decimal place) Also, what is the minimal cost to produce 9,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 9,000 units is $ Hint: 1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function. 2. When finding a relationship between L and K in your system of equations, remember that you will want to eliminate to get a relationship between Land K. 3. Round your values for L and K to one decimal place (tenths).

Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 8L0.3 K0.7 Furthemore, the cost function for a facility is given by the function: C(L, K) = 500L + 100K Suppose the monthly production goal of this facility is to produce 9,000 items. In this problem, we will assume 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 = (Show your answer is exactly 1 decimal place) Units of Capital K = (Show your answer is exactly 1 decimal place) Also, what is the minimal cost to produce 9,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 9,000 units is $ Hint: 1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function. 2. When finding a relationship between L and K in your system of equations, remember that you will want to eliminate to get a relationship between Land K. 3. Round your values for L and K to one decimal place (tenths).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 8L0.3 K0.7 Furthemore, the cost function for a facility is given by the function: C(L, K) = 500L + 100K Suppose the monthly production goal of this facility is to produce 9,000 items. In this problem, we will assume 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 = (Show your answer is exactly 1 decimal place) Units of Capital K = (Show your answer is exactly 1 decimal place) Also, what is the minimal cost to produce 9,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 9,000 units is $ Hint: 1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function. 2. When finding a relationship between L and K in your system of equations, remember that you will want to eliminate to get a relationship between Land K. 3. Round your values for L and K to one decimal place (tenths).
Transcribed Image Text:Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 8L0.3 K0.7 Furthemore, the cost function for a facility is given by the function: C(L, K) = 500L + 100K Suppose the monthly production goal of this facility is to produce 9,000 items. In this problem, we will assume 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 = (Show your answer is exactly 1 decimal place) Units of Capital K = (Show your answer is exactly 1 decimal place) Also, what is the minimal cost to produce 9,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 9,000 units is $ Hint: 1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function. 2. When finding a relationship between L and K in your system of equations, remember that you will want to eliminate to get a relationship between Land K. 3. Round your values for L and K to one decimal place (tenths).
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