Answer to Question #350145 in Calculus for Vickie

Question

The fixed cost of a company is 35000 and the variable cost per unit is 500 and the revenue function for sale is X units is given by R(x)=5000X-100X²

I) find the profit function

Ii) break even values

III)the values of X which results in a loss

Answer 1

(i)

Given $\text{TFC of product} = 35\,000$, $\text{TVC} = 500x$, where $x=\text{no. of units of product}$, $\text{required cost function} = C(x)=35\,000+500x$.

Given $R(x)=5\,000x-100x^2$.

Thus $P(x)=R(x)-C(x)=5\,000x-100x^2-35\,000-500x$,

$P(x)=4\,500x-100x^2-35\,000$

(ii)

For breakeven point, $P(x)=0$ $\Rightarrow$ $4\,500x-100x^2-35\,000=0$ $\Rightarrow$ $x=10, x=35$.

(iii)

For loss, $P(x)<0$ $\Rightarrow$ $x^2-45x+350>0$ $\Rightarrow$ $x>35$ or $x<10$.