Question

The demand equation for a certain product is given by p = 132 - 0.01 x , where p is the unit price (in dollars) of the product and x is the number of units produced. The total revenue obtained by producing and selling x units is given by R = x p.

Determine prices p that would yield a revenue of 9990 dollars.
please i am so confused

Answer 1

So we have\[p=132-.01x\] and \[R=xp\]
Plugging in the equation for p into the equation for R we get:\[R=x(132-.01x)=-.01x ^{2}+132x\]
Now if you plug in the value R=9990, you get:\[9990=-.01x ^{2}+132x\] which is a quadratic equation. Can you take it from here?

Answer 2

I get that part, would the number of sunglasses sold be the x intercept at 9990? and would i then plug it into the price formula?

Answer 3

Yes, you find x which is the number produced and plug that back into the equation for p to find the price. I looks like you'll get a positive and negative root for x? I didn't actually do it myself but the numbers look like they'd go that way with -132. Anyway, the negative answer you may throw out since you can't produce negative sunglasses. Lots of people forget to consider whether the answers they find fit the problem in real world applications.

Answer 4

Thank you for your help. Could you by chance help me set up the parabola for this one?.... A factory is to be built on a lot measuring 150 ft by 200 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory

Answer 5

As in a square lawn? That's what it seems to be saying when it says uniform width i think?

Answer 6

But the factory doesn't fit in a square that size. Not really sure what that's asking. Can you illuminate me?

Answer 7

I think so, i honestly have no idea where to start on this one really. besides that the factory and lawn have the same area within the lot.

Answer 8

(area of lawn)=(area of factory). i am not quite sure how this is possible, with the width being equal distance from factory to edge of lawn all around

Answer 9

Maybe it's nested rectangles/squares and the area of the shapes inside don't count to the total area?

Answer 10

But with the area of the rectangle being the same as the area of the square minus the rectangle. That we could work with and it would be quadratic.

Answer 11

I have no idea to be honest i have been doing this problem for like two days now on and i cannot figure out how to set it up as being quadratic

Answer 12

\[area of lot=150*200=area of factory+area of lawn\]

Answer 13

Did you say the factory and lawn areas were equal? Or was that an assumption?

Answer 14

Well, I told you in an earlier email how to set it up, you need to label your picture with your knowns and unknowns. After that you can set up your equation because you know area is length times width and the factory and lawn have to be the same area (hint: each are half). - message from my teacher

Answer 15

Let me draw something and see what you think.