Question

The revenue, in thousands of dollars, that a company earns selling lawnmowers can be modeled by R(x)=90x-x² and the company's total profit, in thousands of dollars, after selling x lawnmowers can be modeled by P(x)=-x²+30x-200. Which function represents the companys cost, in thousands of dollars, for producing lawnmowers?(Recall that profit equals revenue minus cost.)

A. C(x)=-60x²-200
B. C(x)=60x+200
C. C(x)=2x²+60x+200
D. C(x)=-2x²-60x-200

Answer 1

The cost function for producing lawnmowers, denoted as C(x), is found by subtracting the profit function from the revenue function. The calculation results in the cost function C(x)=60x+200, which corresponds to option B.

Step-by-step explanation:

The company's cost function is determined by subtracting the profit function from the revenue function, as profit is defined as total revenue minus total cost. We are given the revenue function R(x)=90x-x² and the profit function P(x)=-x²+30x-200. To find the cost function, C(x), we rearrange the profit equation to be P(x)=R(x)-C(x), which yields C(x)=R(x)-P(x). Substituting the given functions into this equation results in C(x)=(90x-x²)-(-x²+30x-200) simplifying to C(x)=90x-x²+x²-30x+200, which then simplifies further to C(x)=60x+200. Therefore, the correct answer is B. C(x)=60x+200.