## Related questions with answers

Two people decide to open a business reconditioning toner cartridges for copy machines. They rent a building for $7000/year and estimate that building maintenance, taxes, and insurance will cost$6500/year. Each person wants to make $12/h in the first year and will work 10 h per day for 260 days of the year. Assume that it costs$28 to restore a cartridge and that the restored cartridge can be sold for $45. How many cartridges must the business restore and sell annually to break even, not including the hourly wage the owners wish to earn?

Solution

VerifiedIn order to break even, Cost to operate ($C$) should be equal to total revenue($R$).

If $n$ is the number of cartridges to be sold in order to beak even, then:

$\begin{align*} 13500 + 28n &= 48n\\ 13500 &= 20n \\ n&= \dfrac{13500}{20}\\ n &= 675 \end{align*}$

Hence, $\text{\textcolor{#4257b2}{675 cartridges}}$ should be sold annually to break even.

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