Question

A company has found that when $x$ units of a product are manufactured and sold, its revenue is given by $x^2+100x$ dollars and its costs are given by $240x+500$ dollars. How many units must be produced and sold to make a profit of $10,000$ dollars? (Hint: profit $=$ revenue-costs)

Answer 1

Let us use profit $=$ revenue $-$ costs to find a formula for the profit $P$
$P=(x^2+100x)-(240x+500)$

Substitute $P$ in the above equation by $10,000$ dollars to obtain
$10000=x^2-140x-500$

$x^2-140x-10500=0$

$x=194.10$ and $x=-54.01$

The number of units to produce must be positive, so
$x=194$.