1. The problem statement, all variables and given/known data A company sells running shoes to dealers at a rate f $40 per pair if fewer than 50 pairs are ordered. If a dealer orders 50 or more pairs (up to 600), the price per pair is reduced at a rate of 4 cents times the number ordered. What size order will produce the maximum amount of money for the company? 2. Relevant equations Vertex Formula -- -(b/2a) 3. The attempt at a solution My experience from other problems like this is that the charge should be set as x and the amount of shoes sold should be y. In order to figure out the number of shoes sold (y), I can create two points...but I think this is where I'm confused. Initially I wanted to use (40,49) and (39.96, 51). However, the problem states the discount is a rate of 4 cents times the number ordered. For example if I ordered 100 shoes, I'd pay $36 for each one (100*.04 is 4). If I get two good points, I could get a slope, set up my equation for y and multiply that by x. Then I can use the vertex formula. I'm just having trouble figuring out how to write up this equation. Thank you!