Question

A guitar factory has a cost of productio c(x)=75x+50,000. If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up to the nearest dollar and write

Answer 1

$409

Explanation:

You want the break-even selling price of a guitar if production cost is c(x) = 75x+50000 and x=150 units are sold.

Break even

To break even, the revenue must be equal to the cost. If P is the price of each guitar, then the revenue is ...

R(x) = Px

To break even, we have ...

R(x) = C(x)

150P = 75(150) +50000

P = 75 +50000/150 = 75 +333.33 = 408.33

The selling price of each guitar should be $409 to break even.

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Additional comment

The cost equation tells you the production cost for a guitar is $75, and there is overhead cost of $50,000. Effectively, the overhead must be divided by the number of units sold, and that allocated cost is added to the actual production cost of a guitar to get the break-even selling price.

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