   Chapter 9, Problem 88RE 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.Evaluate and explain the meanings of(a) lim x → ∞ C ( x ) .(b) lim x → ∞ C ¯ ( x ) = lim x → ∞ C ( x ) x .

(a)

To determine

To calculate: The value of the limit, limxC(x), where C(x)=60x+70000 represents the cost function of the company and what the value means.

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. The function R¯(x)=R(x)x represents the average revenue per unit of the company and the function C¯(x)=C(x)x represents the average cost per unit of the company.

Formula used:

A limit limxcx can be simplified as,

limxcx=c

Calculation:

(b)

To determine

To calculate: The value of the limit, limxC¯(x), where C¯(x) represents the average cost per unit of the company and what it means.

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