Question

You are starting a part-time business. You make an initial investment if $9,000. The unit cost of the product is $6.90, and the selling price is $13.15. A) find equations for the total cost C (in dollars) for x units. C(x)= B) find the break even point (in units) C) how many units would yield a profit of $1,500?

Answer 1

We set x equal to the no. of units.

a)

The total cost price = Initial investment + Unit cost price * number of units

Replacing the values:

The total cost price = 9,000+ 6.90*x

Therefore:

C(x)=9,000+ 6.90x

c)

Profit = total selling price - total cost price

We need a profit of 1,500

Therefore:

Profit = 1.500

1.500 = 13.15x - C(x)

1.500 = 13.15x - 9,000+ 6.90x

1,500 = 6.25x - 9,000

1,500 + 9,000 = 6.25x

Solve for x

10,500= 6.25x

10.500/6.25 = x

x=1680

Therefore, 1680 units must be produced to get a profit of $1,5000