Question

A company makes pencils. they sell each pencil for $10.

Their revenue is represented by R= 10x
The cost to make the pencils is $3 each with a one time start up cost of $5000.
Their cost is represented by C= 3X+5000

1.Find the profit, P, (P=R-C) when the company sells 1000 pens.
2. Find the number of pens they need to sell to break even ( when R=C)

Answer 1

We have the profit fomula:

P = R - C

= $10.x - ($3.x + 1000)

= $7.x - 1000

1. If the company sells 1000 pens:

P = $7 . 1000 - $1000

= $6000

2. If they want to break even:

P at least = 0

Assume P = 0

=> $7.x - $1000 = 0

=> x = 1000/7 ≈ 142,86

So if they want to break even, they have to sell at least 143 pens