SOLUTION: The bici bicycle company is planning to make a low price ultra-light bicycle. There are two different plans being considered for this building this bicycle. The first plan includes

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Question 796638: The bici bicycle company is planning to make a low price ultra-light bicycle. There are two different plans being considered for this building this bicycle. The first plan includes a cost of $125000 to design and build a prototype bicycle. The materials and labor costs for each bike made under the first plan will be $225. The second plan includes a cost of $100000 to design and build the prototype. The materials and labor costs for each bike made under the second plan will be $275.
You recently got a job at brick bicycle company as a financial analyst. You have been asked to analyze the costs for each proposed bicycle prototype and determine which plan bici should follow. Use any method to determine your response.
Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website!
Assume n bicycles of each plan.
x = total cost for first plan;
y = total cost for second plan.

First plan: 125000+225n=x

Second plan: 100000+275n=y

We might want to know, for how many produced bicycles would the two plans be of equal cost. Equate x and y, and solve for n.

We can use this found value of n to calculate which plan is more expensive for quantity of bikes less than n; and we can calculate which plan is more expensive for quantity of bikes greater than n.

Starting this, if , then ,

. This is how many bikes produced of each plan would make the plans equal in cost.

Now, you can test x and y for and for and see how the plans compare.
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=?
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=?, and the "400" is just arbitrarily chosen.
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=?, and again, the "600" is arbitrary.
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=?