Solve the Problem. -A Company That Produces Handbags Has Found That Revenue from That

Multiple Choice

Solve the problem.
-A company that produces handbags has found that revenue from the sales of the handbags is $4 per handbag, less sales costs of $100. Production costs are $125, plus $3 per handbag. Profit (P) is given by revenue (R) less cost (C) , so the company must find the production level x that makes
P > 0, that is, R - C > 0.
(a) Write an expression for revenue, R, letting x represent the production level (number of handbags to be produced.)
(b) Write an expression for production costs C in terms of x.
(c) Write an expression for profit P, and then solve the inequality P > 0.
(d) Describe the solution in terms of the problem.

A)
(a) R = 4x - 100;
(b) C = 125 - 3x;
(c) P = ( 4x - 100) - ( 125 - 3x) = x - 175; x > 175;
(d) To make a profit, more than 175 handbags must be produced and sold.
B)
(a) R = 4x - 100;
(b) C = 75 + 5x;
(c) P = ( 4x - 100) - ( 75 + 5x) = x - 125; x > 125;
(d) To make a profit, more than 125 handbags must be produced and sold.
C)
(a) R = 4x - 100;
(b) C = 125 + 3x;
(c) P = ( 4x - 100) - ( 125 + 3x) = x - 225; x > 225;
(d) To make a profit, more than 225 handbags must be produced and sold.
D)
(a) R = 4x + 100;
(b) C = 125 + 3x;
(c) P = ( 4x + 100) - ( 125 + 3x) = x - 25; x > 25;
(d) To make a profit, more than 25 handbags must be produced and sold.