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Production The production function for a company is given by f(x, y) = 100x0.6,0.4 where x is the number of units of labor (at $72 per unit) and y is the number of units of capital (at $48 per unit). The total cost for labor and capital cannot exceed $100,000. (a) Find the maximum production level for this manufacturer. (Round your answer to the nearest integer.) units (b) Find the marginal productivity of money. (Round your answer to three decimal places.) (c) Use the marginal productivity of money to find the maximum number of units that can be produced when $125,000 is available for labor and capital. units (d) Use the marginal productivity of money to find the maximum number of units that can be produced when $320,000 is available for labor and capital. units A manufacturer has an order for 1000 units of fine paper that can be produced at two locations. Let x, and x, be the numbers of units produced at the two locations. The cost function is modeled by C = 0.1x₁² + 25x₁ + 0.05x2² + 48×2. Find the number of units that should be produced at each location to minimize the cost. ×₁ = units units

Production The production function for a company is given by f(x, y) = 100x0.6,0.4 where x is the number of units of labor (at $72 per unit) and y is the number of units of capital (at $48 per unit). The total cost for labor and capital cannot exceed $100,000. (a) Find the maximum production level for this manufacturer. (Round your answer to the nearest integer.) units (b) Find the marginal productivity of money. (Round your answer to three decimal places.) (c) Use the marginal productivity of money to find the maximum number of units that can be produced when $125,000 is available for labor and capital. units (d) Use the marginal productivity of money to find the maximum number of units that can be produced when $320,000 is available for labor and capital. units A manufacturer has an order for 1000 units of fine paper that can be produced at two locations. Let x, and x, be the numbers of units produced at the two locations. The cost function is modeled by C = 0.1x₁² + 25x₁ + 0.05x2² + 48×2. Find the number of units that should be produced at each location to minimize the cost. ×₁ = units units

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 6SC: A company that makes and sells baseball caps has found that the total monthly cost C in dollars of...
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Production The production function for a company is given by f(x, y) = 100x0.6,0.4 where x is the number of units of labor (at $72 per unit) and y is the number of units of capital (at $48 per unit). The total cost for labor and capital cannot exceed $100,000. (a) Find the maximum production level for this manufacturer. (Round your answer to the nearest integer.) units (b) Find the marginal productivity of money. (Round your answer to three decimal places.) (c) Use the marginal productivity of money to find the maximum number of units that can be produced when $125,000 is available for labor and capital. units (d) Use the marginal productivity of money to find the maximum number of units that can be produced when $320,000 is available for labor and capital. units
Transcribed Image Text:Production The production function for a company is given by f(x, y) = 100x0.6,0.4 where x is the number of units of labor (at $72 per unit) and y is the number of units of capital (at $48 per unit). The total cost for labor and capital cannot exceed $100,000. (a) Find the maximum production level for this manufacturer. (Round your answer to the nearest integer.) units (b) Find the marginal productivity of money. (Round your answer to three decimal places.) (c) Use the marginal productivity of money to find the maximum number of units that can be produced when $125,000 is available for labor and capital. units (d) Use the marginal productivity of money to find the maximum number of units that can be produced when $320,000 is available for labor and capital. units
A manufacturer has an order for 1000 units of fine paper that can be produced at two locations. Let x, and x, be the numbers of units produced at the two locations. The cost function is modeled by C = 0.1x₁² + 25x₁ + 0.05x2² + 48×2. Find the number of units that should be produced at each location to minimize the cost. ×₁ = units units
Transcribed Image Text:A manufacturer has an order for 1000 units of fine paper that can be produced at two locations. Let x, and x, be the numbers of units produced at the two locations. The cost function is modeled by C = 0.1x₁² + 25x₁ + 0.05x2² + 48×2. Find the number of units that should be produced at each location to minimize the cost. ×₁ = units units
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