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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

Revenue A newly released film has its weekly revenue given by

R ( t ) = 50 t t 2 + 36 ,    t 0 where R is in millions of dollars and t is in weeks.

(a) After how many weeks will the weekly revenue be maximized?

(b) What is the maximum weekly revenue?

(a)

To determine

To calculate: The number of weeks after which the weekly revenue be maximized.

Explanation

Given Information:

The equation for weekly revenue is given as

R(t)=50tt2+36, t0

Where, R is in millions of 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 revenue is given as

R(t)=50tt2+36, t<

(b)

To determine

To calculate: The amount of maximum weekly revenue.

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