Answer
a) $x=7500$ units
b) $x\gt 7500$ units
Work Step by Step
We are given:
$R(x)=12x$
$C(x)=10x+15,000$
a) Find the break-even point:
$R(x)=C(x)$
$12x=10x+15,000$
$12x-10x=10x+15,000-10x$
$2x=15,000$
$x=\dfrac{15,000}{2}$
$x=7500$
b) Find the number of units that must be sold to earn a profit:
$R(x)>C(x)$
$12x\gt 10x+15,000$
$12x-10x\gt 10x+15,000-10x$
$2x\gt 15,000$
$x\gt \dfrac{15,000}{2}$
$x\gt 7500$
