Question

Given C(x)=145x+70,560R(x)=285xWhat is the number of units that must be produced and sold to break even? What is the amount coming in and going out? What is the profit function?

Answer 1

SOLUTION

(a) To break even, total revenue must be equal to total cost.

So we equate the revenue function to the cost function and find x which is the number of units, we have

$\begin{gathered} C(x)=145x+70,560 \\ R(x)=285x \\ 145x+70,560=285x \\ 70,560=285x-145x \\ 140x=70,560 \\ x=\frac{70,560}{140} \\ x=504\text{ units} \end{gathered}$

Hence number of units sold to break even is 504 units

Amount coming and going out, we put x for 504 into any of the equation, we have

$\begin{gathered} R=285\times504 \\ R=143,640 \end{gathered}$

Hence the answer is 143,640

The profit function, we subtract cost function from revenue, we have

$\begin{gathered} P(x)=285x-(145x+70,560) \\ P(x)=285x-145x-70,560 \\ P(x)=140x-70,560 \end{gathered}$

Hence the answer is

P(x) = 140x - 70,560