Answer to Question #192695 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

The Profit function $P(x)$ is the difference between the revenue function $R(x)$ and the total cost function $C(x)$

$$P(x)=R(x)-C(x)$$

Marginal revenue

$$MR(x)=R'(x)=-0.6x+76.16$$

$$R(x)=\int MR(x)dx=\int(-0.6x+76.16)dx$$

$$=-0.3x^2 +76.16x+k$$

$$R(0)=0=>k=0$$

$$R(x)=-0.3x^2+76.16x$$

Total cost

$$C(x)=R(x)-P(x)$$

$$C(x)=-0.3x^2+76.16x$$

$$-(-0.3x^2+56.16x-638)$$

$$=20x+638$$

The total cost for the company to produce 10 items

$$C(10)=20(10)+638=838$$

The total cost for the company to produce 10 items is $\$838.$