Expert: Sherman D. - 1/10/2008

Question
QUESTION: a.   Suppose that a market research company finds that at 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 your answer in the form p = mx + b. (Hint: Write an equation using two points in the form (x,p)).

ANSWER: (42,20)(52,10)

m = (10 - 20)/(52 - 42)
m = (-10)/(10)
m = -1

20 = -1(42) + b
20 = -42 + b
b = 62

ANS: y = -x + 62

---------- FOLLOW-UP ----------

QUESTION: using trial and error how would I find the quanity of tile sets per month that yeilds the highest profit?

Answer
i'd say find the midpoint. The reason for this is.

as x tiles increase p would have to decrease, and if p increased the x tiles would have to increase. the only place that the 2 values coincide is at the midpoint.

(42,20) and (52,10)
M = (52 + 42)/2, (20 + 10)/2
M = (94/2),(30/2)
M = (47,15)

So if i would have to guess 47 tiles at $15.