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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

A cable TV company has 4000 customers paying $110 each month. If each $1 reduction in price attracts 50 new customers, find the price that yields maximum revenue. Find the maximum revenue.

To determine

To calculate: The price that yields maximum revenue and the maximum revenue if a cable TV company has 4000 customers paying $110 each month.

Explanation

Given Information:

A cable TV company has 4000 customers paying $110 each month and each $1 reduction in price attracts 50 new customers.

Formula used:

If f(x) and g(x) are two differentiable functions then by the property of derivative:

ddx(f(x)+g(x))=ddxf(x)+ddxg(x)

And

ddxxn=nxn1

Where n is a constant and x is the variable.

Calculation:

Assume that there are x new customers then the revenue can be written as:

Revenue=(number of customers)(price paid by each customer)=(4000+x)(110x)R(x)=440,000+1500x50x2

The absolute maxima and absolute minima will occur only at the critical points. To calculate the critical points of the revenue function, find the first derivative of the function:

R(x)=440,000+1500x50x2ddx(R)=ddx(440,000+1500x50x2)

Use ddx(f(x)+g(x))=ddxf(x)+ddxg(x)

R(x)=ddx(440,000)+

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