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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning