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(approximately ) must be produced and sold to make a profit of $10,000$ dollars?

• A. $194$
• B. $78$
• C. $87$
• D. $96$

Answer 1

The correct option is A $194$

Let us use profit $=$ revenue $-$ costs to find a formula for the profit $P$

$\Rightarrow$ $P=(x^2+100x)-(240x+500)$

Substitute $P$ in the above equation by $10,000$ dollars to obtain

$\Rightarrow$ $10000=x^2-140x-500$

Write the equation in standard form and solve for $x$

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

Solve the above equation for $x$

$\Rightarrow$ $x=194.10$ and $x=-54.01$

The number of units to produce must be positive, so

$\therefore$ $x=194.$