Obtain breakeven Points

Question

a)A certain company has fixed costs of Kshs 15,000 for its product and variable cost by Kshs

(140+0.04𝑥)per unit, where x is the number of units. The selling price of the product is given

by Kshs (300−0.06𝑥)per unit.Obtainthe breakeven points

Answer 1

Break even points are when the cost equals the sales price. Obviously, you aren't going to make any money if that happens but it is necessary to understand so that you can determine the optimum number of units to manufacture.

Total cost = fixed cost + variable cost

You are told the fixed cost. To determine the variable cost you take the "variable cost per unit" and multiply it by the number of units, so (140 + 0.04x)(x) = 140x + 0.04x²

Total cost = 15000 + 140x + 0.04x²

Your selling price is (300 - 0.06x) multiplied by the number of units so (300 - 0.06x)(x) = 300x - 0.06x²

Break even means cost = sales therefore:

15000 + 140x + 0.04x² = 300x - 0.06x²

To solve a quadratic, move everything to one side setting the quadratic equal to zero:

15000 + 140x + 0.04x² - 300x + 0.06x² = 0 and combine like terms to get:

0.10x² - 160x + 15000 = 0

You can now either factor the quadratic or use the quadratic formula. I'll choose to factor:

Multiply both sides by 10 to get:

x² - 1600x + 150000 = 0

(x - 1500)(x - 100) = 0

Set each factor equal to zero:

x - 1500 = 0 meaning x = 1500 and x - 100 = 0 meaning x = 100

So, the break even points are when you make 100 units and when you make 1500 units. When you manufacture less than 100 units, your cost will be more than your revenue (so you'll lose money). If you make more than 1500 units, again your cost will be more than your revenue. Only when you manufacture between 100 and 1500 units will you make a profit.