   Chapter 10.3, Problem 5E ### 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

# (a) If the total revenue function for a hammer is R  = 36 x − 0.01 x 2 , then sales of how many hammers, x, will maximize the total revenue in dollars? Find the maximum revenue.(b) Find the maximum revenue if production is limited to at most 1500 hammers.

(a)

To determine

To calculate: The maximum revenue of the provided revenue and number of units that is x for the cost function R(x)=36x0.01x2.

Explanation

Given Information:

The provided revenue function is:

R(x)=36x0.01x2

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:

Consider the revenue function R(x)=36x0.01x2.

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

R=36x0.01x2ddxR=ddx(36x0

(b)

To determine

To calculate: The maximum revenue of the provided revenue function R(x)=36x0.01x2 when production is limited for x hammers.

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