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A manufacturer spends z thousand pesos on labor and capital. The number of units of labor obtained by the manufacturer is determined by a function L(a) and the number of units of capital obtained by the manufacturer is determined by a function C(r). Assume that L(r) and C(x) are differentiable functions. The total units of productivity P of the manufacturer is determined by the equation P = 15L04C0.6 The following are known: • When the manufacturer spends 200, 000 pesos on labor and capital, they will have 200 units of labor and 150 units of capital. It is also observed that in this particular scenario, increasing the expenditure r further would increase the labor L at a rate of 1.2 units per thousand pesos, and increase the capital C at a rate of 1.5 units per thousand pesos. • When the manufacturer spends 300, 000 pesos on labor and capital, they will have 450 units of labor and 250 units of capital. It is also observed that in this particular scenario, increasing the expenditure r further would increase the productivity P at a rate of 30 units per thousand pesos. dP when x 200. Round your answers to four decimal dr (a) Find and interpret P and places. IP dự (b) If C(x) attains a local maximum at r = 300, what is when r = 300? Round your answer to four decimal places. Interpret this value in the context of the problem.

A manufacturer spends z thousand pesos on labor and capital. The number of units of labor obtained by the manufacturer is determined by a function L(a) and the number of units of capital obtained by the manufacturer is determined by a function C(r). Assume that L(r) and C(x) are differentiable functions. The total units of productivity P of the manufacturer is determined by the equation P = 15L04C0.6 The following are known: • When the manufacturer spends 200, 000 pesos on labor and capital, they will have 200 units of labor and 150 units of capital. It is also observed that in this particular scenario, increasing the expenditure r further would increase the labor L at a rate of 1.2 units per thousand pesos, and increase the capital C at a rate of 1.5 units per thousand pesos. • When the manufacturer spends 300, 000 pesos on labor and capital, they will have 450 units of labor and 250 units of capital. It is also observed that in this particular scenario, increasing the expenditure r further would increase the productivity P at a rate of 30 units per thousand pesos. dP when x 200. Round your answers to four decimal dr (a) Find and interpret P and places. IP dự (b) If C(x) attains a local maximum at r = 300, what is when r = 300? Round your answer to four decimal places. Interpret this value in the context of the problem.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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3. A manufacturer spends z thousand pesos on labor and capital. The number of units of labor obtained by the manufacturer is determined by a function L(x) and the number of units of capital obtained by the manufacturer is determined by a function C(x). Assume that L(r) and C(r) are differentiable functions. The total units of productivity P of the manufacturer is determined by the equation P = 15L04C0.6 The following are known: • When the manufacturer spends 200, 000 pesos on labor and capital, they will have 200 units of labor and 150 units of capital. It is also observed that in this particular scenario, increasing the expenditure r further would increase the labor L at a rate of 1.2 units per thousand pesos, and increase the capital C at a rate of 1.5 units per thousand pesos. • When the manufacturer spends 300, 000 pesos on labor and capital, they will have 450 units of labor and 250 units of capital. It is also observed that in this particular scenario, increasing the expenditure r further would increase the productivity P at a rate of 30 units per thousand pesos. (a) Find and interpret P and dP when r 200. Round your answers to four decimal dr places. (b) If C(x) attains a local maximum at r = 300, what is when a = 300? Round TP de your answer to four decimal places. Interpret this value in the context of the problem.
Transcribed Image Text:3. A manufacturer spends z thousand pesos on labor and capital. The number of units of labor obtained by the manufacturer is determined by a function L(x) and the number of units of capital obtained by the manufacturer is determined by a function C(x). Assume that L(r) and C(r) are differentiable functions. The total units of productivity P of the manufacturer is determined by the equation P = 15L04C0.6 The following are known: • When the manufacturer spends 200, 000 pesos on labor and capital, they will have 200 units of labor and 150 units of capital. It is also observed that in this particular scenario, increasing the expenditure r further would increase the labor L at a rate of 1.2 units per thousand pesos, and increase the capital C at a rate of 1.5 units per thousand pesos. • When the manufacturer spends 300, 000 pesos on labor and capital, they will have 450 units of labor and 250 units of capital. It is also observed that in this particular scenario, increasing the expenditure r further would increase the productivity P at a rate of 30 units per thousand pesos. (a) Find and interpret P and dP when r 200. Round your answers to four decimal dr places. (b) If C(x) attains a local maximum at r = 300, what is when a = 300? Round TP de your answer to four decimal places. Interpret this value in the context of the problem.
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