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A manufacturer's total production of a new product is P(L, K) = 1500L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $100, a unit of capital $400, and the total budget for labor and c. $360,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? $ (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier.

A manufacturer's total production of a new product is P(L, K) = 1500L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $100, a unit of capital $400, and the total budget for labor and c. $360,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? $ (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier.

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
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 3SC: In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175...
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A manufacturer's total production of a new product is P(L, K) = 1500L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $100, a unit of capital $400, and the total budget for labor and capital is $360,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? $ (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in labor, L, by one unit. O The Lagrange multiplier is the approximate increase in the total budget for labor and capital resulting from an increase in the optimal value of P by one unit. The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in the total budget for labor and capital by one unit. O The Lagrange multiplier is the approximate increase in capital, K, resulting from an increase in the optimal value of P by one unit. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in capital, K, by one unit.
Transcribed Image Text:A manufacturer's total production of a new product is P(L, K) = 1500L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $100, a unit of capital $400, and the total budget for labor and capital is $360,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? $ (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in labor, L, by one unit. O The Lagrange multiplier is the approximate increase in the total budget for labor and capital resulting from an increase in the optimal value of P by one unit. The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in the total budget for labor and capital by one unit. O The Lagrange multiplier is the approximate increase in capital, K, resulting from an increase in the optimal value of P by one unit. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in capital, K, by one unit.
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