Question

A company that manufactures guitars has a fixed cost of $100,000. It costs $100 to produce each guitar and the selling price is $300 per guitar.
a. Write the cost function, C.

b. Write the revenue function, R.


c. What is the break-even point. What does this mean?

Answer 1

a. Write the cost function:: C(x) = 100x + 100,000 where x is number of guitars

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b. Write the revenue function:: R(x) = 300x where x is number of guitars

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c. Find the profit function.

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = [ R(x) ] - [ C(x) ]

P(x) = [ 300x ] - [ 100x+100,000 ]

P(x) = 300x - 100x-100,000

P(x) = 200x - 100,000

The break even point is when the profit is 0 dollars. You don't lose any money. And you don't gain any money.

Solve 125x - 100,000 = 0

125x = 100,000

x = 800 (# of guitars made and sold)