Question

The SneakerRama Company makes and sells sneakers. They have one linear function that represents the cost of producing sneakers and another linear function that models how much income they get from those sneakers. Describe the key features that would determine if these linear functions ever intercepted.

Answer 1

think this is math am i correct?

Answer 2

Hopefully, the slope of the function that describes the cost of manufacturing the shoes is less than the slope of the function that describes the revenue from selling the shoes. If it is, then the more shoes they sell, the more profit they make.

If the lines intersect, and the slopes are as I described (higher slope for the revenue), any point to the right of the intersection is a point where a profit is made: the revenue from selling the shoes is greater than the cost of making them.

An example is attached. In the example, the cost of making the shoes is 3000+3x, representing a startup cost of 3000 (buying the shoe-making machine and renting a factory building), and 3 per pair of shoes manufactured. On the sales side, the revenue is -500 + 20x, representing 500 spent on advertising, and a sales price of 20 per pair of shoes sold. The break-even point (where the lines intersect) is the point where
3000+3x=−500+20x
3500=17x
x≈205.9
So after 206 pairs are sold, the operation starts turning a profit.

Answer 3

http://assets.openstudy.com/updates/attachments/5322600de4b04b5f5fab0df5-whpalmer4-1394780200170-shoes.png

Answer 4

Hahahah, Yes this is math. Thanks for the help.