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#1 2007-03-14 15:40:18

Monique
Member
Registered: 2007-02-17
Posts: 22

can someone help through this so can help my daughter on the weekend??

The revenue (ie income recieved - cost of production) recieved by a company from the sale of a certain product is given by the equation

R = 1500p - 50p ( p has a "power of 2" dont know how to show this)       where R is the revenue in dollars and p is the selling price(in $).

a)  Sketch the graph of R = 1500p - 50p (p to the power of 2)


b)  Use the graph to find the maximum revenue the company can expect from sales of the product.

c)  Use the graph to find the price at which the product must be sold to achieve this.


d) describe in your own words the relationship between revenue and the selling price for this product.faintfaint

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#2 2007-03-14 18:06:02

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: can someone help through this so can help my daughter on the weekend??

What you mean is

right? if so , it's a parabola
, the coefficient of the 2 power p is negative , which indicates that the parabola is downward(I am not sure if you understand what I mean , I am not very good at explaining detail)
Then it has a maximum value whose x-coordinate is equal to
where a=-50 ,b=1500

Last edited by Stanley_Marsh (2007-03-14 18:06:24)


Numbers are the essence of the Universe

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#3 2007-03-15 16:36:26

Monique
Member
Registered: 2007-02-17
Posts: 22

Re: can someone help through this so can help my daughter on the weekend??

no, it is set as R = 1500p - 50p(with the p  attached to the 50 having a power of 2)swear

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#4 2007-03-15 23:51:21

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: can someone help through this so can help my daughter on the weekend??

That's what Stanley said, he just switched the terms around to put them in order of... order. smile

Anyway, the easiest way of doing this would be to put different values of p into the equation and see what R comes out. Each time you do that, you can plot a point on your graph of p against R and once you have enough points you can join them up. 0 to 30 is the range that you should be looking at.

Once you have the graph drawn, b) and c) should be easy, assuming you've drawn it accurately enough. You just look at the point where the graph is highest, and then look for the value of p that does that.

d) just needs you to describe the shape of the graph. Once you've drawn the thing, that shouldn't be too hard either.


Why did the vector cross the road?
It wanted to be normal.

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#5 2007-03-19 14:48:26

Monique
Member
Registered: 2007-02-17
Posts: 22

Re: can someone help through this so can help my daughter on the weekend??

thanks guys - we've managed to plot the graph and from what we can work out its a downward graph with maximum revenue of $14 250 when the selling price is $15? This right?dizzy

anyway can anyone please tell us how we would describe the relationship between revenue and the selling price for this product based on the shape of this graph?

there's a maximun peak so how would i describe this?dunno

Last edited by Monique (2007-03-19 14:49:21)

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#6 2007-03-19 15:53:17

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: can someone help through this so can help my daughter on the weekend??

you should discuss two situation ,if p is smaller than the peak , as p increases ,R also increases , if p is larger than the peak
as p increase , R decreases.


Numbers are the essence of the Universe

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#7 2007-03-19 21:51:35

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: can someone help through this so can help my daughter on the weekend??

You must have made a small error somewhere, because I get that the maximum revenue should be $11,250. You got the selling price right though.

As for describing the trend, I'd just say that $15 is the optimum selling price, and the revenue drops depending on how far the selling price is from that.


Why did the vector cross the road?
It wanted to be normal.

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