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 Raiiderx October 29th, 2013 12:03 PM

Algebra Question

My question below:

I have not done any form of mathematics for a while, so I am rusty. Please suggest any basic principles I could research to help further my understanding in this field. I ask this as part 2 honestly makes no word of sense to me, but by requesting the answer I hope I can break it down and see where certain values are coming from.

Part 2: We now consider the cost of manufacturing the articles. Suppose that the relationship between price and demand is still P = 20 - 3d and that the cost £C thousand of manufacturing d thousand is given by C = 9 + 4d. The revenue £R thousand accruing from selling d thousand articles is calculated by: revenue = articles sold * price of article. The profit £N thousand from such sales is given by: profit = revenue - cost of
manufacturing.

(a) Use these definitions of revenue and profit to derive quadratic expressions for R and N in terms of d. Draw the graphs of R and N with d for values of d between 0 and 6.

(b) For what values of d is N zero? Calculate the range of values of d for which the company makes a profit and find the corresponding article price range. What is the maximum profit? What is the demand, and what is the article price, at which the maximum profit is achieved?

Here are the previous questions, I think I have the correct answers for these:

Part 1:

The price at which a company sells a particular article varies with the quantity it sells. If it charges £14 per article, it sells 2000 articles; if it charges £5 per article it will sell 5000 articles. Let the quantity of articles the company sells be denoted by the variable d (measured in thousands of articles) and let the price be £p.

(a) Construct a set of axes with d as the horizontal axis and p as the vertical axis. Plot the points (2,14) and (5,5) with respect to these axes and derive the equation of the line to be p = 20 - 3d .

(b) The company decides that it is worthwhile to increase the supply of such articles as the price increases. If the price is £5 it is prepared to supply 3000 articles, at a price of £9 it is prepared to supply 7000 articles. Let the supply of articles by the company be denoted by the variable s (measured in thousands of articles).
Construct a set of axes with s as the horizontal axis and p as the vertical axis. Plot the points (3,5) and (7,9) with respect to these axes. Derive the equation of the straight line joining these points.

(c) By solving a set of two simultaneous equations find the price at which supply is equal to demand. What is the demand at such a price?

 icemanfan October 29th, 2013 12:16 PM

Re: Algebra Question

If I understand correctly, revenue should be $d(20 - 3d)$ and cost should be $9 + 4d$, so profit is then $N= d(20 - 3d) - (9 + 4d)$, which is a parabola. To determine what value of d yields maximum profit, you have to find the vertex of the parabola. Do you know how to do that?

 Raiiderx October 29th, 2013 01:42 PM

Re: Algebra Question

I can't say I do, I have come across the parabola before, but working out vertex is new to me. Please do educate.

Also, does this relate to part 2 question A or B?

 skipjack October 30th, 2013 12:16 AM

It relates to 2(a). Do you know how to produce the requested graphs?

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