Question

A small software company invests $16,000 to produce a software package that will sell for $49.75. Each unit costs $7.40 to produce. (Round your answers to the nearest whole number.)(a) How many units must the company sell to break even?(b) How many units must the company sell to make a profit of $90,000?

Answer 1

Answer:

$378,1748$

Step-by-step explanation:

GIVEN: A small software company invests $\ 16,000$ to produce a software package that will sell for $\ 49.75$. Each unit costs $\ 7.40$ to produce. (Round your answers to the nearest whole number).

TO FIND: (a) How many units must the company sell to break even?(b) How many units must the company sell to make a profit of $\ 90,000$?

SOLUTION:

Fixed cost for production of Software package $=\ 16000$

Selling price of Software package $=\ 49.75$

price of producing each unit of software package $=\ 7.4$

Let total units sold be $x$

Total profit $=(\ 49.75-\ 7.4)x-\ 16000$

                  $=\ 42.35x-\ 16000$

(a)

for company to break even, $\text{Total profit}=0$

                       $\ 42.35x-\ 16000=0$

                       $\ 42.35x=\ 16000$

                       $x=\frac{16000}{42.35}$

                      $x\approx378$

company will have to sell at least $378$ units.

(b)

for company to make total profit of $\ 90000$

                       $\ 42.35x-\ 16000=\ 90000$

                      $x=\frac{74000}{42.35}$

                      $x\approx1748$      

company will have to sell at least $1748$ units