Question

The function P(x)=-30x^2+360+785 models the profit, P(x), earned by a theatre owner on the basis of a ticket price, x. Both the profit and ticket price are in dollars. What is the maximum profit, and how much should the tickets cost?

Answer 1

ok :)
do u know differentiation?

Answer 2

never heard of it

Answer 3

this is not calculus math

Answer 4

oh okk :)
we can do it the other way
in this way you have to use smart vision e.e
ready?

Answer 5

@imqwerty sure, what's the second way of doing this?

Answer 6

ok note this-\[p(x)=-30x^2 +360+785\]

i'll tell step by step
x^2 will always be positive
do u agree?

Answer 7

yes

Answer 8

ok

and -30x^2 will also be negative
do you agree?

Answer 9

yes

Answer 10

ok

more the x more will be the value of -30x^2
agreed?

Answer 11

What do you mean by "more the x more the value of -30x^2" ?

Answer 12

@imqwerty ^

Answer 13

I don't understand your question

Answer 14

ok
try putting x=1 and x=2
then find the value of -30x^2 that u get

Answer 15

am i putting x=1 into this equation? :
p(x)=−30x2+360+785

Answer 16

no
jst put x=1 and then x=2 in -30x^2
and tell what u get

Answer 17

-30x^2

-30(1)^2
=-30

-30(2)^2
=-120

Answer 18

yes can you conclude that more the value of x lesser wil -30x^2 become
note that -120 is lesser than -30

Answer 19

oh okay i see

Answer 20

How do i find the maximum profit?

Answer 21

are you sure the middle term is 360 - not 360x ?

Answer 22

@welshfella Yes it is 360x , not negative 360x

Answer 23

ok
now see this -\[p(x)=-30x^2+360+785\]

here only negative term is -30x^2
the more its negative the more it will decrease the profit

its max value can be 0 when x=0
so x=0
damn it its 360x!

Answer 24

with 360 it would make the function a parabola opeeing downwards with a maximum turning point

Answer 25

@imqwerty okay, so what must I solve for? I'm a bit confused right now
@welshfella mhm...

Answer 26

wth 360x i meant to say

Answer 27

well to find the maximum by completing the square and converting the equation to vertex form

Answer 28

or you could use -b/2a which gives the x coordinate value when the function is a maximum

Answer 29

@shelby1290: P(x)=-30x^2+360+785 is a quadratic function. Because the sign of the greatest power of x is negative, the graph of this function opens DOWN. We need only find the x value at which the profit is a maximum. Yes, finding x = -b/(2a) will give you that x-value. Graphing P(x)=-30x^2+360+785 may help you to visualize what is happening.
Please identify coefficients a and b in P(x)=-30x^2+360+785.

Answer 30

@welshfella alright so like this?
P(x)=(-30x^2+360x)+785
=-30(x^2+360x)+785
=-30(x^2-12x)+785
=-30(x^2-12x+36-36)+785
=-30(x^2-12x+36)-23550+785
=-30(x^2-12x+36)-22765
=-30(x-12)(x-12)-22765
=-30(x-12)^2-22765

Answer 31

@mathmale
-b/2a
= -(360)/2(-30)
= -360/-60
=6

Answer 32

Then calculate x=-b/(2a). Once you have that, calculate P(x).
You've done a lot of work to complete the square. Can you explain the significance of your results?
If your calculations are correct, your work gives you both the ticket cost for max profit and the actual max. profit.

Answer 33

Here you've found that x=6 (6 tickets). But when you completed the square, you found that x=12. You're on the right track, but both of your results (x=6, x=12) can't be right.
If you have a graphing calculator, graph P(x)=-30x^2+360+785 and determine from the graph the x value at which the graph has a max.

Answer 34

I think I made a mistake because the maximum profit is $1865

Answer 35

I don't have a graphing calculator with me

Answer 36

Again, one result or the other (x=6, x=12) MAY be correct, but not both. Besides graphing P(x)=-30x^2+360+785, what other ways have you for finding the max. of P(x)?

Answer 37

Looking at P(x)=-30x^2+360x+785, I see that a = -30 and b=360. These values disagree with yours. Can you explain why?

Answer 38

I've only learned how to find the max by finding the vertex, which is by completing the square

Answer 39

OK, then. Let's look at the given function again: P(x)=-30x^2+360x+785. Before we move on, please double check to ensure that this equation is the correct one.

Answer 40

OH i see where i made a mistake now

Answer 41

What mistake was that?

Answer 42

=-30(x^2+360x)+785
=-30(x^2-12x)+785
=-30(x^2-12x+36-36)+785
=-30(x^2-12x+36)+1080+785
=-30(x^2-12x+36)+1865
=-30(x-12)(x-12)+1865
=-30(x-12)^2+1865


I didn't multiply -36 by -30 to get 1080
and then 1080 +785 =1865

Answer 43

$1865 is the max profit

Answer 44

Think you can fix this yourself? How could I help you further? Are you done now, or have y ou more work to do on this particular problem?

Answer 45

yes - good work

Answer 46

I believe that's all I have to do because the question is only asking for the max profit and how much the tickets should cost

Answer 47

Good for y ou! See you again. Bye.

Answer 48

@Shelby1290 have you checked your messages?