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
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Chapter1: Functions And Models
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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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