   Chapter 9, Problem 85RE 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

Cost, revenue, and profit In Problems 85-88, assume that a company’s monthly total revenue and total cost (both in dollars) are given by R ( x )   = 1 4 0 x   −   0 . 0 1 x 2   a n d   C ( x )   =   60 x +   7 0 , 0 0 0 where x is the number of units. Let P(x) denote the profit function.Find (a) lim x → 4000 R ( x ) , (b) lim x → 4000 C ( x ) , and (c) lim x → 4000 P ( x ) .

(a)

To determine

To calculate: The value of the limx4000R(x), where R(x)=140x0.01x2.

Explanation

Given Information:

A company’s monthly total revenue is represented by the function R(x)=140x0.01x2. The company’s total cost function is represented by C(x)=60x+70000.

Formula used:

A limit limxcx can be simplified as,

limxcx=c

Calculation:

Consider the provided revenue function,

R(x)=140x0.01x2

Consider the provided limit,

limx4000R(x)=limx4000(140x0

(b)

To determine

To calculate: The value of the limx4000C(x), where C(x)=60x+70000.

(c)

To determine

To calculate: The value of the limit limx4000P(x), where P(x) is the profit function for the company.

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