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

Multiple Choice

Solve the problem.
-A company that produces appliances has found that revenue from the sales of the appliances is $80 per appliance, less sales costs of $200. Production costs are $350, plus $70 per appliance. 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 appliances 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 = 80x - 200;
(b) C = 350 + 70x;
(c) P = ( 80x - 200) - ( 350 + 70x) = 5x - 550; 5x > 550; x > 110
(d) To make a profit, more than 110 appliances must be produced and sold.
B)
(a) R = 80x + 200;
(b) C = 350 - 70x;
(c) P = ( 80x + 200) - ( 350 - 70x) = 10x - 150; 10x > 150; x > 15
(d) To make a profit, more than 15 appliances must be produced and sold.
C)
(a) R = 80x - 200;
(b) C = 350 + x;
(c) P = ( 80x - 200) - ( 350 + 90x) = 10x - 500; 10x > 500; x > 50
(d) To make a profit, more than 50 appliances must be produced and sold.
D)
(a) R = 80x - 200;
(b) C = 350 + 70x;
(c) P = ( 80x - 200) - ( 350 + 70x) = 10x - 550; 10x > 550; x > 55
(d) To make a profit, more than 55 appliances must be produced and sold.