SOLUTION: Please help me to help my son."Quadratic Equations and functions"_word problem. "A manufacturer determines that the number of drills it can sell is given by the formula D= -5p^2+52

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Question 25147: Please help me to help my son."Quadratic Equations and functions"_word problem. "A manufacturer determines that the number of drills it can sell is given by the formula D= -5p^2+520p-240 where p is the price of the drills in dollars.
a) At what price will the manufacturer sell the maximum number of drills?
b) What is the maximum number of drills that can be sold?
I hope that I typed this correctly. It should read as D= -5p squared, etc. Also, the answer is on a graph. ????? Thank you for your help.

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
D+=+-5p%5E2%2B520p-240

to "solve" this - as a purely theoretical question, we want to know where the curve crosses the x-axis, ie where y is zero. In your question you are using D instead of y, so where is D=0...

0+=+-5p%5E2%2B520p-240
and re-arranging gives
5p%5E2+-+520p+%2B+240+=+0
p%5E2+-+104p+%2B+48+=+0
this does not factorise, so use the quadratic formula.

This produces 2 answers for p, namely p=0.465 and p=103.535.

Now any quadratic is a symmetrical curve so, the maximum lies mid-way between these 2 values... namely at (0.465+103.535)/2 --> p=52.
So, the price at which it sells the maximum number of drills is $52
This corresponds to D=-%2852%29%5E2+%2B+520%2852%29+-+240 drills
D+=+-2704+%2B+27040+-+240 drills
D = 24096 drills

As for a graph... pick a few values of p, put each into the equation as i did and find corresponding values of D then plot them.

jon.