Question

Stuck on a test question that I'm not entirely sure how to do. Any help?
Ms. Ortiz sells tomatoes wholesale. The function p(x) = -80x^2 + 320x - 10, graphed below, indicates how much profit she makes on a load of tomatoes if she sells them for 4-x per kilogram.

Answer 1

http://gyazo.com/349fb957951c3c212cf323155e093afc.png picture link

Answer 2

Then it says "what should Ms.Ortiz charge per kilogram of tomatoes to make the maximum profit, and what is the maximum profit she can make on a load of tomoatoes.

Answer 3

My guess is
$230 at $3 per kilogram
$310 at $2 per kilogram**
$320 at $2 per kilogram
$320 at $3 per kilogram

Answer 4

min/max values tend to bring about derivatives, or at least a vertex

Answer 5

do you know the structure/shape of a quadratic equation? do you know what a derivative of a function is?

Answer 6

No really no. I've been trying to get help from my teacher but it isn't going too well.

Answer 7

hmm, you should have had some work that relates to finding the roots of a quadratic equation at least.

can you tell me some things that you have been studying with regards to quadratic equations?

Answer 8

or, if you just want to try out the options; let x = 2, and then 3 to see what values they produce, then pick the biggest one

Answer 9

I have the formula \[x= \frac{ -b \pm ?\sqrt{(b)^{2}-4(a)(c)}}{2(a)}\]

Answer 10

I got really lost on the parabola and graphs part of the lesson though.

Answer 11

that would tell us an interval, and the middle of that interval would be the x value

Answer 12

\[0=-80x^2 + 320x - 10\]
\[0=-8x^2 + 32x - 1\]
\[0=8x^2 - 32x + 1\]
that might help to reduce the numbers to play with

Answer 13

Ohhh I see! So plug them in to see what higher number you get?

Answer 14

32 +- sqrt(32^2 -4(1)(8))
-----------------------
2(8)

32 +- sqrt(992)
---------------
2(8)

the midpoint (average) of these end points is



32 - sqrt(992) 32 + sqrt(992)
-------------- + -------------
2(8) 2(8)
-------------------------------
2

32+32
---------
2(2)(8)


2(32) 32
--------- = ---- = 2
2(2)(8) 16

Answer 15

shorrtcut .... yeah, see what x=2, and x=3 get you; then pick the highest value

Answer 16

I got x=3 is 230 and x=2 is 310

Answer 17

So B would be the right answer?

Answer 18

good, then 310 at 2 is correct :)

Answer 19

Thank you so much!

Answer 20

youre welcome, and good luck :)