   Chapter 2.2, Problem 64E

Chapter
Section
Textbook Problem

Profit from Sale of Smartphones Apollo manufactures smartphones at a variable cost ofV(x) = 0.000003x3 − 0.03x2 + 200xdollars, where x denotes the number of units manufactured per month. The monthly fixed cost attributable to the division that produces them is $100,000. The total revenue realized by Apollo from the sale of x smartphones is given by the total revenue functionR(x) = −0.1x2 + 500x (0 ≤ x ≤ 5000)where R(x) is measured in dollars. a. Find a function C that gives the total cost inclined by the manufacture of x smartphones. b. Find the total profit function. c. What is the profit when 1500 units are produced and sold each month? (a) To determine To find: The function C which gives the total cost incurred by the manufacture of x smartphones. Explanation Given information: The variable cost by the Apollo manufacture smartphones is, V(x)=0.000003x30.03x2+200x The monthly fixed cost is$100,000 .

The revenue function by the Apollo manufacture of x smartphones is,

R(x)=0.1x2+500x,(0x5000)

Calculation:

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

C(x)=V(x)+100000

Substitute 0

(b)

To determine

To find: The total profit function.

(c)

To determine

To find: The profit when 1500 units are produced and sold each month.

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