Question

Marginal profit. Crawford Computing finds that its weekly profit, in dollars, from the production and sale of x laptop computers is $P(x)=-0.004 x^{3}-0.3 x^{2}+600 x-800$ Currently Crawford builds and sells 9 laptops weekly. a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 8 laptops weekly? c) What is the marginal profit when $x=9 ?$ d) Use the answers from parts (a) $-(c)$ to estimate the profit resulting from the production and sale of 10 laptops weekly.

Name: Problem 7, Chapter 2: Calculus and Its Applications
Uploaded: 2021-06-09T16:13:42-08:00
Duration: 3 min 58 s
Channel: Donald Albin

   Marginal profit. Crawford Computing finds that its weekly profit, in dollars, from the production and sale of
x laptop computers is $P(x)=-0.004 x^{3}-0.3 x^{2}+600 x-800$
Currently Crawford builds and sells 9 laptops weekly.
a) What is the current weekly profit?
b) How much profit would be lost if production and sales dropped to 8 laptops weekly?
c) What is the marginal profit when $x=9 ?$
d) Use the answers from parts (a) $-(c)$ to estimate the profit resulting from the production and sale of
10 laptops weekly.

Calculus and Its Applications

Marvin L. Bittinger,… 10th Edition

Chapter 2, Problem 7

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Solved by Expert Donald Albin

06/09/2021

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004 x^{3}-0.3 x^{2}+600 x-800$. Show more…

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Marginal profit. Crawford Computing finds that its weekly profit, in dollars, from the production and sale of x laptop computers is $P(x)=-0.004 x^{3}-0.3 x^{2}+600 x-800$ Currently Crawford builds and sells 9 laptops weekly. a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 8 laptops weekly? c) What is the marginal profit when $x=9 ?$ d) Use the answers from parts (a) $-(c)$ to estimate the profit resulting from the production and sale of 10 laptops weekly.

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Key Concepts

Profit Function

A profit function expresses a company's profit as a function of the number of units produced or sold. It models how revenue and costs interact, allowing businesses to assess profitability at different production levels.

Marginal Profit

Marginal profit is the rate at which profit changes as production increases by one unit. In calculus, it is represented by the derivative of the profit function with respect to quantity and indicates the additional profit from producing and selling one more unit.

Derivative

A derivative measures the instantaneous rate of change of a function with respect to a variable. In economics, it helps determine how a small change in production quantity will affect profit, cost, or revenue.

Linear Approximation

Linear approximation uses the derivative at a specific point to estimate the function's value near that point. This is particularly useful in estimating the effect of producing one additional unit when changes are small.

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