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

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) (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
RELATED QUESTIONS
Simple Interest: I can do the math if I knew how to set this up I think. I have setup... (answered by venugopalramana)

I have looked for this problem on this site but did not see it anyplace. Please help.... (answered by solver91311)

I think this is the right section to put this, can I please be shown how to solve a... (answered by josgarithmetic,ikleyn,MathTherapy,solver91311)

I asked this problem already and received an answer, but my teacher has said I need to... (answered by stanbon)

can you tell me how to find the LCM the easiest way? I have looked at all your examples... (answered by stanbon)

Hello, I'm swamped here. I am really no good at math. I have to show the steps to this (answered by doukungfoo)

Hello, I am taking some practice test for the College placement test and I am having... (answered by longjonsilver)

hello, I would be extremely grateful for any help or advice for this problem. It has... (answered by stanbon)

i am supposed to take a test for college that has linear equations such as c+(4-3c)-2=0... (answered by Theo)