Question

a company that sells phones generates revenue given by the function r(x) = x² + 20x + 50 (where x is the number of phones produced per month). the cost of production is given by the function c(x) = 50x + 30. which function gives the profit earned by the company? a. x² + 70x + 80 b. x² + 70x + 20 c. x² - 30x + 20 d. x² + 30x + 20

Explanation:

Step1: Recall Profit Formula

Profit \( P(x) \) is revenue minus cost, so \( P(x)=r(x)-c(x) \).

Step2: Substitute Functions

Given \( r(x)=x^{2}+20x + 50 \) and \( c(x)=50x + 30 \), substitute into the profit formula:
\( P(x)=(x^{2}+20x + 50)-(50x + 30) \).

Step3: Simplify the Expression

Distribute the negative sign: \( x^{2}+20x + 50-50x - 30 \).
Combine like terms: \( x^{2}+(20x-50x)+(50 - 30)=x^{2}-30x + 20 \).

Answer:

C. \( x^{2}-30x + 20 \)