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Expert: - 10/1/2010


Question
Suppose a market research company finds that a price of p=$20, they
would sell x=42 tiles each month. If they lower the price to p=$10, then
more people would purchase the tile, and they can expect to sell x=52
tiles in a month's time. Find the equation of the line for the demand
equation. Write you answer in the form p=mx+b. Hint. Write an equation
using two points in the form (x,p)

Substitute the result found from part a. into the equation R=xp to find the
revenue equation. Provide your answer in simplified form

Answer
Well, at $20 there would be 42 and at $10, there would be 52.  By a drop in $10,  10 more would be sold.  This means that for every decrease of $1, there is an increase of 1 sold.

This means the price + number sold = constant.  Note that
20 + 42 = 62 and 10 + 52 = 62.  This means n, the number sold,
is defined as n = 62 - p.

The equation for cash flow would be c = np.
Since n = 62 - p, c = (62-p)p = 62p - p^2.

We have c(p) = 62p - p^2, so find c'(p), set it equal to 0, and this will determine the best price.  Using n = 62 - p, this will be the number to sell.  The value of n can be found using n = 62 - p.

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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