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manuracturer's total production of a new product is P(L, K) = 1800L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is $960,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? %24 (b) Find the value of the Lagrange multiplier.

manuracturer's total production of a new product is P(L, K) = 1800L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is $960,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? %24 (b) Find the value of the Lagrange multiplier.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 6EQ: Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of...
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A manufacturer's total production of a new product is P(L, K) = 1800L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is $960,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? 24 (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. O 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 the optimal value of P resulting from an increase in capital, K, 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.
Transcribed Image Text:A manufacturer's total production of a new product is P(L, K) = 1800L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is $960,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? 24 (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. O 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 the optimal value of P resulting from an increase in capital, K, 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.
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