Question

A cell phone manufacturer makes profits (P) depending on the sale price (s) of each phone The function P=-s^2+120s-2000 models the monthly profit for a flip phone from Cellular Heaven. What is the maximum profit possible for the manufacturer?
A: 1600
B:100
C:60
Please help! Thank you so much!

Answer 1

so \(\bf P=-s^2+120s-2000\)
notice, what kind of graph do you think that would be?

Answer 2

I think it is some type of quadratic functions graph. I think it will have a parabola with a minimum and maximum value.

Answer 3

yes, the squared term coefficient is negative that is \(\bf -s^2\) as opposed to \(\bf s^2\)

that means the parabola is going downwards over the y-axis, like

so notice the graph

P "profits" go up and up and up, depending on what S "sale price" is set to
so the peak is at the parabola vertex
that is, as high as P can get is up to the vertex, or the "hump" of the parabola

Answer 4

you can get the vertex "x and y" coordinates of a parabola over the y-axis like so by using \(\bf \left(-\cfrac{b}{2a}, c-\cfrac{b^2}{4a}\right)\\
\)
x y

Answer 5

-s^2+120s-2000
a b c

Answer 6

so you really don't need to know the "sale price" S, just the maximum profit P
so you'd want the "y" coordinate only

Answer 7

I think it is 1600. I am sorry if I am wrong! I am trying to understand! Thank you so much for all you are doing for me!

Answer 8

so, what did you get?

Answer 9

I think it is 1600. I am sorry if I am wrong! I am trying to understand! Thank you so much for all you are doing for me!

Answer 10

\(\bf c-\cfrac{b^2}{4a} \implies (-2000)-\left(\cfrac{120^2}{4(-1)}\right)\)

Answer 11

did you get 1600?

Answer 12

Yes I did

Answer 13

\(\bf c-\cfrac{b^2}{4a} \implies (-2000)-\left(\cfrac{120^2}{4(-1)}\right) \implies (-2000) + 3600 = 1600\)

Answer 14

Thank you so much! I got that answer! You were such great help!

Answer 15

yw