A manufacturer's total production of a new product isP(L, K) = 1500L2/3K1/3where 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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Description: A manufacturer's total production of a new product isP(L, K) = 1500L2/3K1/3where 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 capita

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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.

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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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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