a. Suppose a market research company finds that at a price of p = $30, they would sell x = 32 baskets each month. If they lower the price to p = $10, then more people would purchase the baskets, and they can expect to sell x = 52 baskets 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).

Question

a. Suppose a market research company finds that at a price of p = $30, they would sell x = 32 baskets each month. If they lower the price to p = $10, then more people would purchase the baskets, and they can expect to sell x = 52 baskets 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 1

I think the equation should be

x = mp+b

since the price is set, and the demand follows.

x(30) = 32
x(10) = 52

32 = 30p + b
52 = 10p + b

20p = -20
p = -1
b = 62

x = -p + 62
or, if you have a sales goal you want to meet, you can figure the price you must set by
p = -x + 62