Quadratic function word problem with given equation.

[calcdummy]

Homework Statement

The profit, P, of a video company, in thousands of dollars is given by P=-5x^2+550x-5000, where x is the amount spent on advertising in thousands of dollars.

a) Determine the amount spent on advertising that will result in a profit of $0.

Homework Equations

P=-5x^2+550x-5000

The Attempt at a Solution

P=-5x^2+550x-5000
0=-5x(x-110)-5000
-5x=0 or x-110=0
x=0 or x=110

Therefor when the amount of $110 thousand is spent there will be a profit of $0.

This answer kind of confuses me but on the graph it appears to be accurate. Could someone please review this and tell me if I am incorrect and what I could do to correct it? Thank you in advance.

 

[scurty]

You have the right idea by setting the equation equal to 0! However, what you did is not valid. Try plugging in x=0 and x=110 into the original equation and see what answer you get (it won't be 0).

Since 0=-5x^{2} + 550x - 5000 is a quadratic function (as you pointed out in the topic title), do you know of any formulas that can solve for x? (were there any you went over in class for this section?)

 

[calcdummy]

You have the right idea by setting the equation equal to 0! However, what you did is not valid. Try plugging in x=0 and x=110 into the original equation and see what answer you get (it won't be 0).

Since 0=-5x^{2} + 550x - 5000 is a quadratic function (as you pointed out in the topic title), do you know of any formulas that can solve for x? (were there any you went over in class for this section?)

Well I'm home schooled so I'm basically teaching myself all of this. But could I use the quadratic formula to figure out the amount spent to get a profit of zero (x)?

 

[scurty]

Ah, okay. But, yes, the quadratic formula is what you can use in this case.

Alternatively, you can factor the equation which is probably the preferred method since using the quadratic formula will give you big numbers. Can you simplify you equation at all to make the numbers smaller to work with?

 

[calcdummy]

I simplified it to -5(x^2-110x+1000) <- is that correct?

with that I tried to use the quadratic formula. Not sure if I was on the right track but I tried anyway... and got:

-(-110)±√-110^2-4(1)(1000)/2(1)

110±√12100-4000/2

110+90/2 or 110-90/2

x=145 or x=65

 

[tal444]

110+90/2 or 110-90/2

Everything is right up to here. You forgot to divide 110 by 2 also. Remember, you must divide ALL the terms.

 

[e^(i Pi)+1=0]

edit - already answered ^

 

[calcdummy]

Hi tal! Thank you for your response. So would that make x=100 & x=10? Also, would my final answer be "In order for the video company to make a profit of $0 they must spend either ten thousand dollars or a hundred thousand dollars in advertisements."?

 

[tal444]

Seems right to me.