A manufacturer determines that the number of drills it can sell is given by the formula D= -3p^2 + 180p - 285, 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?

Question

A manufacturer determines that the number of drills it can sell is given by the formula D= -3p^2 + 180p - 285, 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?

anonymous · Answer

Let's do part A first.  Differentiate D(p) with respect to p.  Then set it to 0 and solve for p.

anonymous · Answer

moneybird, seriously, can we not just give answers away?

anonymous · Answer

i am a little confused by how you worded it, can you try explaining? thank you so much!

anonymous · Answer

Do you know how to find the minimum/maximum of a function?

anonymous · Answer

no, we were told to just graph them and then find the min/max, but I don't know how to do it when it comes to a word problem

anonymous · Answer

OK, if you're looknig at a graph of the function (a) is asking, at what X value is the function maximized?  and (b) is asking, what is the Y value of that function at that X value?

anonymous · Answer

Okay that makes sense because i just realized p and d are x and y. But i tried graphing it and it's too big to see, so there's no finding the values. How can i do it the way you and moneybird did?

anonymous · Answer

The way we did it is calculus, but that won't make sense unless you are already taking a calculus class.

anonymous · Answer

oh ok, i was searching this earlier and someone was trying to do it with the quadratic formula, can i do it with that? (this is algebra II)

anonymous · Answer

hmm, probably not.  the quadratic formula would tell you at what price the number of drills you sell is 0.

anonymous · Answer

what do you suggest i do??

anonymous · Answer

when you say "the graph is too big", what are you using to graph it?  just graph it using a different settings or something.

anonymous · Answer

ok i tried that and i got 30 for x (max) and -381 for y(min) is the right? i feel like the -381 isn't right..

anonymous · Answer

no, the price can't be negative

anonymous · Answer

that would mean they're giving you money for taking the drill :-)

anonymous · Answer

haha, ok well the 30 is right and its on the y axis, and then i go to find the minimum it is also on the y axis and thats what the negative is..is it supposed to be on the x? or would it not be a min value then?