equation problem

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June 8th 2012, 01:21 PM
allison

equation problem

(Hi) hello i would appreciate if someone could kindly look into the problem and help me get the solution:

Q) the profit, P, of a video company (in thousands of dollars) is given by P(x)=-5x² + 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. In other words,you will determine the amount that must be spent on advertising in order for the company to "break even." Describe the relationship between these values and the graph of P(x)
June 8th 2012, 01:30 PM
Reckoner

Re: equation problem

Quote:

Originally Posted by allison

a) Determine the amount spent on advertising that will result in a profit of $0. In other words,you will determine the amount that must be spent on advertising in order for the company to "break even." Describe the relationship between these values and the graph of P(x)

The company will break even when the profit $P(x) = 0$ . So we have an equation:

$P(x) = 0$

$\Rightarrow-5x^2+550x-5000 = 0$

Now solve for $x$ .
June 8th 2012, 01:30 PM
skeeter

Re: equation problem

Quote:

Originally Posted by allison

(Hi) hello i would appreciate if someone could kindly look into the problem and help me get the solution:

Q) the profit, P, of a video company (in thousands of dollars) is given by P(x)=-5x² + 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. In other words,you will determine the amount that must be spent on advertising in order for the company to "break even." Describe the relationship between these values and the graph of P(x)

set P(x) = 0 and solve the quadratic for x

also, please post algebra questions in the algebra forum, not in the introduction lobby.
June 8th 2012, 01:51 PM
allison

Re: equation problem

thank you so much guys! that was really quick

So, for x.. what i have done is

- 5x2 + 550x - 50000
or -5 (x2-110x+1000)
or, -5 (x-100)(x-10)
or,x=100, or x=10

i guess i have to findout the mid-value as well inorder to get the amt.
so, mid-value is x = 100+10 divided by 2
so x = 55

am i right, guys?? pls help
June 8th 2012, 01:57 PM
allison

Re: equation problem

thnx skeeter! i am a new user so didn't pay much attention to it ,i will make sure next time i will posts my queries into proper forum. could you kindly look into my answer whether that is how it should be
June 8th 2012, 02:11 PM
Reckoner

Re: equation problem

Quote:

Originally Posted by allison

or,x=100, or x=10

This is correct.

Quote:

Originally Posted by allison

i guess i have to findout the mid-value as well inorder to get the amt.
so, mid-value is x = 100+10 divided by 2

No. We are looking for what value(s) of $x$ make $P(x)$ zero. You have found that there are two values for which this occurs: $x=10$ and $x=100$ . Both of these are break-even points. The first solution is the minimum amount of money that must be spent on advertising in order to turn a profit, and the second solution is the maximum amount of money that can be spent on advertising before the advertising costs outweigh the increased revenue.

Finding the midpoint of these two values actually gives you the x-coordinate of the vertex of this parabola, which in this problem represents the amount of money that must be spent to get the maximum profit.
June 8th 2012, 02:26 PM
allison

Re: equation problem

Quote:

Originally Posted by Reckoner

This is correct.

No. We are looking for what value(s) of $x$ make $P(x)$ zero. You have found that there are two values for which this occurs: $x=10$ and $x=100$ . Both of these are break-even points. The first solution is the minimum amount of money that must be spent on advertising in order to turn a profit, and the second solution is the maximum amount of money that can be spent on advertising before the advertising costs outweigh the increased revenue.

Finding the midpoint of these two values actually gives you the x-coordinate of the vertex of this parabola, which in this problem represents the amount of money that must be spent to get the maximum profit.

Thank you so much for your time ! that was really helpful.
June 8th 2012, 02:48 PM
allison

Re: equation problem

Hi, just a quick question
how can i insert a division line : i want to insert a line so that i can put 1/2 or 1 over 2. i would like the 1 to be right on top of the 2 with a line separating the numbers in the middle.

thanks for the help!
June 8th 2012, 03:14 PM
allison

Re: equation problem

Hi, just a quick question
how can i insert a division line : i want to insert a line so that i can put 1/2 or 1 over 2. i would like the 1 to be right on top of the 2 with a line separating the numbers in the middle.

thanks for the help!
June 10th 2012, 04:46 AM
allison

Re: equation problem

Quote:

Originally Posted by Reckoner

This is correct.

No. We are looking for what value(s) of $x$ make $P(x)$ zero. You have found that there are two values for which this occurs: $x=10$ and $x=100$ . Both of these are break-even points. The first solution is the minimum amount of money that must be spent on advertising in order to turn a profit, and the second solution is the maximum amount of money that can be spent on advertising before the advertising costs outweigh the increased revenue.

Finding the midpoint of these two values actually gives you the x-coordinate of the vertex of this parabola, which in this problem represents the amount of money that must be spent to get the maximum profit.

Hi, i got the maximum profit as :
mid-value is x = 100+10 divided by 2
so x = 55
P(x)= -5x2 + 550x - 5000
P(55)= - 5(55)2 + 550(55) - 5000
= 15125 + 30250 - 5000
= 45375 - 5000
=40,375
The maximum profit is $40,375.

Can you help me graph the function and state the domain, please.
June 10th 2012, 06:55 AM
Reckoner

Re: equation problem

Quote:

Originally Posted by allison

P(55)= - 5(55)2 + 550(55) - 5000

$P(55)=-5\cdot55^2+550\cdot55-5000$

$=-15\,125+30\,250-5000$

$=10\,125$

Quote:

Originally Posted by allison

Can you help me graph the function and state the domain, please.

The simplest way to sketch a graph is to plot a few points. We already have the coordinates of several important features of this parabola: the vertex is at $(55, 10\,125)$ , the $x$ -intercepts are at $(10, 0)$ and $(100, 0)$ . Setting $x=0$ shows us that our $y$ -intercept is at $(0, -5000)$ . Now plot the points, and connect them with a smooth parabola.

For the domain, note that this is a polynomial function. What is the domain of a polynomial function?