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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

Profit From Sale of Pagers A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $20,000, and the variable cost for producing x pagers/week is

V(x) = 0.000001x3 − 0.01x2 + 50x

dollars. The company realizes a revenue of

R(x) = −0.02x2 + 150x (0 ≤ x ≤ 7500)

dollars from the sale of x pagers/week.

  1. a. Find the total cost function.
  2. b. Find the total profit function.
  3. c. What is the profit for the company if 2000 units are produced and sold each week?

(a)

To determine

To find: The total cost function.

Explanation

Given information:

The weekly fixed cost is $20,000 .

The variable cost to produce x pagers/week by Chapman Corporation is,

V(x)=0.000001x30.01x2+50x

The revenue function is,

R(x)=0.02x2+150x,(0x7500)

Calculation:

The cost function C is the sum of variable cost and the fixed cost.

C(x)=V(x)+20000

Substitute 0

(b)

To determine

To find: The total profit function.

(c)

To determine

To find: The profit for the company when 2000 units are produced and sold each week.

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P-23RECh-2 P-24RECh-2 P-25RECh-2 P-26RECh-2 P-27RECh-2 P-28RECh-2 P-29RECh-2 P-30RECh-2 P-31RECh-2 P-32RECh-2 P-33RECh-2 P-34RECh-2 P-35RECh-2 P-36RECh-2 P-37RECh-2 P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-46RECh-2 P-47RECh-2 P-48RECh-2 P-49RECh-2 P-50RECh-2 P-51RECh-2 P-52RECh-2 P-53RECh-2 P-54RECh-2 P-55RECh-2 P-56RECh-2 P-57RECh-2 P-58RECh-2 P-59RECh-2 P-60RECh-2 P-61RECh-2 P-62RECh-2 P-63RECh-2 P-64RECh-2 P-1BMCh-2 P-2BMCh-2 P-3BMCh-2 P-4BMCh-2 P-5BMCh-2 P-6BM

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