Question

The formulas below are the cost and revenue functions for a company that manufactures and sells small radios. a. Use the formulas shown to write the company's profit function, P, from producing and selling x radios. b. Find the company's profit if 21,000 radios are produced and sold C(x) 224,000+32x and R(x) 46x a. The company's profit function is P(x)-(Simplify your answer.)

Answer 1

a) P(x)=14x-224,000 and b) P(21,000)=70,000.

Explanation:

a.) Use the formulas shown to write the company's profit function, P, from producing and selling x radios.

The company's profit is given by its revenue minus the production cost. Then, the profit function P(x) will be given by

1. 
   `P(x)=R(x)-C(x)=46x-(224,000+32x)=14x-224,000.`

b.) Find the company's profit if 21,000 radios are produced and sold

To obtain the company's profit we just need to substitute the value given (x=21,000) in the formula 1). Therefore,

`P(21,000)=R(21,000)-C(21,000)=14(21,000)-224,000=70,000`.