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# Break-Even Point - Algebra

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1. (Supplement A) Richard Winchester, owner of Winchester Products, is considering whether to produce a new product. He has considered the operations requirements for the product as well as the market potential. Richard estimates the fixed costs per year to be \$40,000 and variable cost for each unit produced to be approximately \$50.

a) If Richard sells the product at a price of \$70, how many units of product does he have to produce and sell in order to break even? Solve both graphically and algebraically.
b) Richard forecasts sales of 3,000 units if the selling price is set at \$70, and 3,800 units if the selling price is set at \$65. Which pricing strategy would you recommend to Richard? Why?

#### Solution Preview

Please see the attachment for the detailed explanation of the answer. The Excel file contains the graphical determination of break-even point.

Solution

a) We can find the break-even point both graphically and algebraically.
It is given that,
Fixed cost, FC = \$40,000
Variable cost per unit, VC = \$50
Selling Price per unit, SP = \$70
Let Q denote the number of units sold. Then the total cost is
Total cost = FC + (VC)Q = 40000 + 50Q
and the total revenue is
Revenue = (SP)Q = 70Q

Since revenue equals ...

#### Solution Summary

The solution explains the graphical and algebraic method for determination of the break-even point.

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