   Chapter 10.4, Problem 11E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# Advertising and sales An inferior product with a large advertising budget sells well when it is introduced, but sales fall as people discontinue use of the product. Suppose that the weekly sales S are given by S = 200 t ( t + 1 ) 2 ,   t ≥ 0 where S is in millions of dollars and t is in weeks. After how many weeks will sales be maximized?

To determine

To calculate: The number of weeks after which the sales get maximizes.

Explanation

Given Information:

The equation for weekly sales is given as

S=200t(t+1)2, t0

Where, S is in dollars and t is in weeks.

Formula used:

To find the maximum value, calculate the relevant stationary value of an equation. Differentiate the function with respect to the independent variable and equate it to 0. the relevant value is the stationary value that satisfies the provided conditions.

Quotient rule gives the derivative of a function when one differentiable function is divided by the other. To find the derivative of a function f(x)g(x), use

ddx[f(x)g(x)]=g(x)f'(x)f(x)g'(x)(g(x))2

Calculation:

The equation for weekly sales is given as

S=200t(t+1)2, t0

To find the stationary value

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