How many units must the company sell to break even; how many units to make profit of $100,000?

Question

A small software development company invests $15,000 to produce a software package that will sell for $51.55. each unit costs $10.25 to produce.

Find how many units the company needs to sell to break even; how.many units does the company need to sell to make a profit of $100,000. Round to nearest whole number.

Answer 1

The profit per unit is 41.30

The profit function is P(n) = 41.30*n - 15000

To break even, P(n) = 0

41.30*n - 15000 = 0

n = 364

Likewise P(n) = 41.30*n - 15000 = 100000

n = 2785

Now, does that $15000 initial investment allow them to produce as many as they want????

15000/10.25 = 1463. They can produce AT MOST 1463 units . They will need 1322 more units

to make the profit of 100,000, which in turn requires for money, which in turn requires more units to be sold