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

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.

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

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

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

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

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

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

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?

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?

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

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

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

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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