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

@HelpBlahBlahBlah

Answer 2

not sure sorry

Answer 3

@jim_thompson5910

Answer 4

@yara26 @whpalmer4

Answer 5

@thomaster

Answer 6

@jigglypuff314

Answer 7

@timo86m

Answer 8

if tthey intercept doesn't that mean they broke even not sure. I cant think right.

Answer 9

I cant really understand the question myself lol

Answer 10

(it's past my bed time)
if slopes are parallel then they never intersect...

so if cost per shoe = income per shoe
then the lines would never intersect

Answer 11

ohh okay thankss!

Answer 12

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 \[3000+3x = -500+20x\]\[3500=17x\]\[x\approx 205.9\]So after 206 pairs are sold, the operation starts turning a profit.