Question

The Oliver Company plans to market a new product. Based on its market studies, Oliver estimates that it can sell up to 5,500 units in 2005. The selling price will be $3 per unit. Variable costs are estimated to be 10% of total revenue. Fixed costs are estimated to be $10,800 for 2005. How many units should the company sell to break even?

Answer 1

Your figure for the fixed costs is somewhat confusing. I will assume you mean $10,800

Revenue Function:

R(x) = 3x

Cost Function:

C(x) = 0.1[R(x)] + 10800
C(x) = 0.1(3x) + 10800
C(x) = 0.3x + 10800

Break-Even Point: R(x) = C(x):

3x = 0.3x + 10800
3x - 0.3x = 10800
2.7x =10800
x = 10800 / 2.7
x = 4000

Break-Even Point = 4,000 units
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Hope this helps