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

Answer:

(a) The profit function is P(x)=14x-224,000.

(b) The company's profit at x=21000 is 70,000.

Step-by-step explanation:

Cost function is

$C(x)=224,000+32x$

Revenue function is

$R(x)=46x$

where, x is number of radios.

(a)

Formula for profit:

Profit = Revenue - Cost

The profit function is

$P(x)=R(x)-C(x)$

$P(x)=46x-(224,000+32x)$

$P(x)=46x-224,000-32x$

$P(x)=14x-224,000$

The profit function is P(x)=14x-224,000.

(b)

Substitute x=21000 in the above equation to find the company's profit if 21,000 radios are produced and sold.

$P(21000)=14(21000)-224,000$

$P(21000)=294000-224,000$

$P(21000)=70,000$

Therefore the company's profit at x=21000 is 70,000.