Explanation
By definition:
• the number of units is x,
,
• the cost function C(x) = 12x + 15,000,
,
• the revenue function R(x) = 32x,
,
• the profit function P(x) = R(x) - C(x).
The break-even point is the point x where we have P(x) = 0. So we must find x such that:
[tex]\begin{gathered} P(x)=R(x)-C(x)=0, \\ 32x-(12x+15,000)=0, \\ 20x-15,000=0, \\ x=\frac{15,000}{20}=750. \end{gathered}[/tex]
We have found that the break-even point is x = 750 units.
Answer
750 units
