Answer to Question #201438 in Calculus for raf

Question

A company's profit function, in dollars, is given by P(x)= -0.3x^2+56.16x-638 where x is the number of items sold. in addition, the company has a marginal revenue function of MR(x)= -0.6x+76.16. determine the total cost for the company to produce 10 items .

Answer 1

since, profit=revenue-cost

This implies,

cost=revenue-profit

Finding revenue function from the given marginal revenue function,

$R(x)=\int MR(x)dx=\int (-0.6x+76.16)dx= -0.3x^2+76.16x+c\newline \text{When items is zero i.e., }x=0, \newline then R(0)=0\implies c=0.\newline R(x)=-0.3x^2+76.16x$

Therefore,

$C(x)=R(x)-P(x)= (-0.3x^2+76.16x)+(-0.3x^2+56.16x-638)=-0.3x^2+132.32x-638\newline C(10)=-0.3(10)^2+132.32(10)-638 =655.2\newline \text{tuhs, total cost for the company to produce 10 items is 655.2.}$