a retail owner can but a certain clock at an average price of $53 per clock and sell them for an average price of $84 per clock. his fixed costs are $8000 per month and his variable cost is $5 per clock. (A) how many clocks must he sell each month to break even? (B) how many clocks must he sell to have a profit of $3000?

The contribution margin is the amount by which the selling price of the clock exceeds the cost of the clock. The contribution margin is used to figure the break-even point, and the amount of profit from sales.

contribution margin = selling price - variable cost - purchase price

contribution margin = $84 -5 -53 = $26

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(A)

To break even, the contribution margin from 'b' clocks must equal or exceed the owner's fixed cost:

26b ≥ 8000

b ≥ 8000/26

b ≥ 307.7

The owner must sell 308 clocks each month to break even.

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(B)

To make a profit of $3000, the owner must sell enough clocks to cover the $8000 fixed cost and contribute an additional $3000. That is, the total contribution margin from selling p clocks must be about $3000+8000 = $11000.

26p ≈ 11000

p ≈ 11000/26 ≈ 423.08

The owner must sell about 423 clocks each month to earn a profit of about $3000.

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Additional comment

Selling 423 clocks will yield a profit of $2998.