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1. Cost Analysis and Production: A factory's weekly production costs y and its weekly production quantity x are related by the equation y² — 5x³ = 4 where y is in thousands of dollars and x is in thousands of units of output. dy dx a. Use implicit differentiation to find a formula for the marginal cost of production. b. Find the marginal cost of production when x=4 and y=18. (Write in the units of measurement.) c. Suppose that the factory begins to vary its weekly production level. Assuming that x and y are differentiable functions of time, t in weeks, dy find a formula for the time rate of change of production costs. 2 dt dy d. Compute when x=4, y=18, and the production level is rising at the rate dt of 0.3 thousand units per week. e. Write a sentence that shows your findings in part d. Be sure to include units of measurement.

1. Cost Analysis and Production: A factory's weekly production costs y and its weekly production quantity x are related by the equation y² — 5x³ = 4 where y is in thousands of dollars and x is in thousands of units of output. dy dx a. Use implicit differentiation to find a formula for the marginal cost of production. b. Find the marginal cost of production when x=4 and y=18. (Write in the units of measurement.) c. Suppose that the factory begins to vary its weekly production level. Assuming that x and y are differentiable functions of time, t in weeks, dy find a formula for the time rate of change of production costs. 2 dt dy d. Compute when x=4, y=18, and the production level is rising at the rate dt of 0.3 thousand units per week. e. Write a sentence that shows your findings in part d. Be sure to include units of measurement.

Calculus: Early Transcendentals
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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1. Cost Analysis and Production: A factory's weekly production costs y and its weekly production quantity x are related by the equation y² – 5x³ : = 4 where y is in thousands of dollars and x is in thousands of units of output. dy 9 dx a. Use implicit differentiation to find a formula for the marginal cost of production. b. Find the marginal cost of production when x=4 and y=18. (Write in the units of measurement.) c. Suppose that the factory begins to vary its weekly production level. Assuming that x and y are differentiable functions of time, t in weeks, dy find a formula for the time rate of change of production costs. " dt dy d. Compute when x=4, y=18, and the production level is rising at the rate dt of 0.3 thousand units per week. e. Write a sentence that shows your findings in part d. Be sure to include units of measurement.
Transcribed Image Text:1. Cost Analysis and Production: A factory's weekly production costs y and its weekly production quantity x are related by the equation y² – 5x³ : = 4 where y is in thousands of dollars and x is in thousands of units of output. dy 9 dx a. Use implicit differentiation to find a formula for the marginal cost of production. b. Find the marginal cost of production when x=4 and y=18. (Write in the units of measurement.) c. Suppose that the factory begins to vary its weekly production level. Assuming that x and y are differentiable functions of time, t in weeks, dy find a formula for the time rate of change of production costs. " dt dy d. Compute when x=4, y=18, and the production level is rising at the rate dt of 0.3 thousand units per week. e. Write a sentence that shows your findings in part d. Be sure to include units of measurement.
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