Math Word Problem

Question

17. A company that sells radio has a yearly fixed cost of $30,000. It costs that company $45 to produce each radio. Each radio will sell for $75. a. Find the company's cost function C(x), where x is the number of the ratios that sold. b. Find the company's revenue function R(x), where x is the number of the ratios that sold. C. Find and interpret (R-C)(x). Find and interpret (R-C)(10000). Does your answer make sense? Find and interpret (R-C)(45,000). Does your answer make sense? Find the break-even point. Please explain your answer as clearly as possible.

Answer 1

C(x) = 30,000 + 45x

R(x) =75x

R(x) -C(x) = 75x - 30000-45x = 30x -3000

R(10000) -C(10000) = 30(10,000) -3000 = 300,000 -3000= $297,000

R(45000) -C(45000) = 30(45,000)-3000= 1350,000 -3000 = $1,347,000

break even point is when R=C

75x = 30000-45x

120x = 30,000

x = 30,000/120 = 3000/12 = 1000/4 = 250

more than x=250 and Profit >0

It all makes sense