A farmer can produce f(x,y) = 126/5x² + y² units of produce by utilizing x units of labor and y units of capital. a) Calculate the marginal productivities of labor and capital when x = 8 and y=11. b) Let h be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from 8 to 8+ h units while keeping capital fixed at 1 units. (c) Use part (b) to estimate the change in production when labor decreases from 8 to 7 units and capital stays fixed at 11 units.
A farmer can produce f(x,y) = 126/5x² + y² units of produce by utilizing x units of labor and y units of capital. a) Calculate the marginal productivities of labor and capital when x = 8 and y=11. b) Let h be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from 8 to 8+ h units while keeping capital fixed at 1 units. (c) Use part (b) to estimate the change in production when labor decreases from 8 to 7 units and capital stays fixed at 11 units.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A farmer can produce \( f(x, y) = 126 \sqrt{5x^2 + y^2} \) units of produce by utilizing \( x \) units of labor and \( y \) units of capital.
(a) Calculate the marginal productivities of labor and capital when \( x = 8 \) and \( y = 11 \).
(b) Let \( h \) be a small number. Use the result of part (a) to determine the approximate effect on production of changing labor from 8 to \( 8 + h \) units while keeping capital fixed at 11 units.
(c) Use part (b) to estimate the change in production when labor decreases from 8 to 7 units and capital stays fixed at 11 units.
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