Q:

The revenue, in thousands of dollars, that a company earns selling lawnmowers can be modeled by R(x)=90x-x^2 and the company's total profit, in thousands of dollars, after selling x lawnmowers can be modeled by p(x)= -x^2+30x-200 . Which function represents the company's cost, in thousands of dollars, for producing lawnmowers? (Recall that profit equals revenue minus cost.)A) C(x)= -60x^2-200B) C(x)= 60x^2+200C) C(x)=2x+60x^2+200D) C(x)= -2x-60x^2-200

Accepted Solution

A:
Profit, P is given by:
P=R-C
where
R is the revenue
C is the cost
this implies that:
C=R-P
from the information given, the revenue and the cost functions are given by:
R(x)=90x²-x

P(x)=30x²-x-200

thus the cost function will be:
C(x)=R(x)-P(x)

substituting our values we shall have:
C(x)=90x²-x-(30x²-x-200)
C(x)=(90x²-30x²-x+x+200)
C(x)=60x²+200
The answer is B