QuestionThe formulas below are the cost and revenue functions for a company that manufactures and sells small radios. $$C(x)=24,000+38 x \text { and } R(x)=40 x$$ 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 20,000 radios are produced and sold. a. The company's profit function is $\mathrm{P}(\mathrm{x})=$ : $\square$ (Simplify your answer.)

Studdy Solution
To find the company's profit when 20,000 radios are produced and sold, substitute $x = 20,000$ into the profit function:
$$P(20,000) = 2(20,000) - 24,000$$
Calculate the result:
$$P(20,000) = 40,000 - 24,000$$ $$P(20,000) = 16,000$$
The company's profit function is $P(x) = 2x - 24,000$.
The company's profit when 20,000 radios are produced and sold is $\boxed{16,000}$.