7. A company manufactures shaving sets for $5 each and sells them for $7 each. How many shaving sets must be sold for the company to recover an initial investement of $45,000 and eam an additional $15,000 as profit?
The company has to sell
$15,000 as profit.
shaving sets to recover an initial investment of $45,000 and earn an additional

$30,000

Step-by-step explanation:

profit = amount of sales - expenses

The company spends $5 on each set. it sells each set for $7.

The profit on each set is $7 - $5 = $2.

For each set the company sells, it makes $2 of profit.

It cost the company $45,000 to start production, and the company wants a profit of $15,000. The company needs to earn $45,000 + $15,000 = $60,000 in profits.

Since the profit per set is $2, the number of sets it needs to sell is

$60,000/$2 = 30,000

30,000 sets

Consider a function of , keeping fixed:

Differentiate with respect to :

The denominator is always positive except in the case of , so the numerator determines where has its critical points. We have

When , we get a maximum curvature of