Question

Suppose you are the manager of a firm. The accounting department has provided cost estimates, and the sales department sales estimates, on a new product. Analyze the data they give you, determine what it will take to break even, and decide whether to go ahead with production of the new product The product has a production cost function C(x)=560x + 17,080 and a revenue function R(x) = 700xThe break-even quantity is ______units.

Answer 1

Consider that the break-even quantity is the one corresponding to which the profit is zero i.e. the production cost becomes equal to the revenue earned.

Equate the functions and solve for the break-even quantity as follows,

$\begin{gathered} C(x)=R(x) \\ 560x+17,080=700x \\ 700x-560x=17,080 \\ 140x=17,080 \\ x=122 \end{gathered}$

Thus, the break-even quantity is 122 units.