   Chapter 9, Problem 104RE Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

In Problems 100-107, cost, revenue, and profit are in dollars and x is the number of units.Revenue The total revenue function for a commodity is given by R = 80 x − 0.04 x 2 .a) Find the marginal revenue function.(b) What is the marginal revenue at x =   100 ?(c) Interpret your answer in part (b).

(a)

To determine

To calculate: The marginal revenue function for a commodity with revenue function, R=80x0.04x2.

Explanation

Given Information:

The revenue function of the commodity is R=80x0.04x2.

Formula used:

The simple power rule for the derivative,

ddx(xn)=nxn1

The rule of derivative for constant multiplication,

ddx[kf(x)]=kddx[f(x)]

The sum or difference rule of the derivative,

ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)]

Calculation:

Consider the provided cost function, R=80x0.04x2.

Use the sum or difference rule of the derivative, to differentiate the provided revenue function,

R=ddx(80x0.04x2)=ddx(80x)ddx(0

(b)

To determine

To calculate: The marginal revenue for 100 commodity when revenue function is, R=80x0.04x2.

(c)

To determine

The interpretation of the marginal revenue for 100 commodities when revenue function is R=80x0.04x2 where x is the number of unit.

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