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?

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.