Question

The produce each product unit, the company spends $2.55 on material and $2.85 on labor. Its total fixed cost is $6000. Each unit sells for $7.05.

What is the smallest number of units that must be sold for the company to realize a profit?

Answer 1

Revenue:
R ( x ) = 7.05 x
Cost :
C ( x ) = 6,000 + 2.55 x + 2.85 x = 6,000 + 5.40 x
7.05 x > 6,000 + 5.40 x
7.05 x - 5.40 x > 6,000
1.65 x > 6,000
x > 6,000 : 1.65
x > 3,636.36
x = 3,637 ( we need a whole number )
Answer: The smallest number of units that must be sold for the company to realize a profit is 3,637.