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Finding a break-even point?


A company that manufactures bicycles has a fixed cost of $100,000. It costs $100 to produce each bicycle. The selling price per bike is $300.
i. Write the cost function, C.
ii. Write the revenue function, R.
iii. Determine the break-even point. Describe what this means.
Note: I get steps i and ii but what gets me confused is whether i have to divide or subtract, see here is the first two parts that i have done in this problem

i. c(x) $100,000 + $100x
ii r(x) = 300x
iii r(x)=c(x)
I need to know this part subtracting 100x from both sides because they don't show how to do this in the book i know I will have to divide my answer i just need to know the set up so that i can understand it. can someone show me the steps that way i can take it from there, i look in the book to see how it would be set up but this book doesn't show you the steps they just write what you have to do but i need to visually see the steps to understand

Parts I and II are correct.

The break-even point is where, as you said, r(x) = c(x)
Let x = number of bicycles produced

Thus,
300x = 100,000 + 100x

Subtract 100x from both sides of the equation, so we get
300x (-100x) = 100,000 + 100x (-100x)
200x = 100,000 + 0

Divide both sides by 200 to get
x = 100,000/200 = 500 bicycles

Just basic algebra here!

[Answer: see above]

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