SOLUTION: Hello, I have looked at this prblem for almost two hours and I can't figure how to form the quadratic! Problem: You can see 30 widgets at $500 per year. Furthermore, you find that

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello, I have looked at this prblem for almost two hours and I can't figure how to form the quadratic! Problem: You can see 30 widgets at $500 per year. Furthermore, you find that      Log On


   

Question 236775: Hello, I have looked at this prblem for almost two hours and I can't figure how to form the quadratic! Problem:
You can see 30 widgets at $500 per year. Furthermore, you find that for each $25 decrease in price you can sell 3 more wigdets. At what price should you sell the widgets to maximize gross income and what will that price be.
I did the long way by sub. in 25 increments and adding 3 to amount sold I came up with Gross income max = $16,875 if you sell for $375 ea. How do I work the equation to get in quadratic form from the beginning?
Thanks - Kristen
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x = "CHANGE in number of widgets"

income = (500 - 25x/3)(30 + x)

FOILing ___ I = 15000 + 250x - 25/3 x^2

the max is on the axis of symmetry ___ x = -b / 2a

x = -250 / 2(-25/3) = 15

selling price = 500 - 25(15)/3 = 375

widgets = 30 + 15 = 45

max income = 375 (45) = 16875