   Chapter 9.4, Problem 47E ### 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

# Revenue Suppose that a wholesaler expects that his monthly revenue, in dollars, for an electronic game will be R ( x ) = 100 x − 0.1 x 2 ,  0 ≤ x ≤ 800 where x is the number of units sold. Find his marginal revenue and interpret it when the quantity sold is (a) x = 300. (b) x = 600.

(a)

To determine

To calculate: The marginal revenue, in dollars for R(x)=100x0.1x2, when x=300 and x is the number of units sold.

Explanation

Given Information:

The given revenue function is R(x)=100x0.1x2.

Formula Used:

The marginal revenue for a function R(x) is given by R(x).

According to sum rule of derivatives,

If

f(x)=u(x)+v(x)

Then,

f(x)=u(x)+v(x)

According to power rule,

If f(x)=xn, then f(x)=nxn1.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Calculation:

Consider the provided revenue function R(x)=100x0.1x2.

The marginal revenue for a function R(x) is given by R(x)

Thus, to calculate the marginal revenue calculate the derivative of the function

(b)

To determine

To calculate: The marginal revenue, in dollars for R(x)=100x0.1x2, when x=600 and x is the number of units sold.

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