Answer:
a rebate of 200 dollars will generate 500 sales
with a revenue of 125,000
Explanation:
We need to maximize the total revenue which is:
TR = Price x Quantity. First we define each of these:
P = (450 - 30X)
Q = (100 + 60X)
Being X the cash rebate
We now replace this into the TR formula:
TR = P x Q = (450 -30X) (100 + 60X)
TR = -1800x2 +27,000x -3,000x + 45,000
TR = -1800x2 +24,000x + 45,000
as this is a quadratic function: a: -1,800 b = 24,000 c = 45,000
the maximum revenue will be at the vertex: -b/2a
-24,000/2(-1,800) = 6.67
now we multiply by 30: 6.67 x30 = 200 dollars
which bring 60 x 6.67 = 400 new customers
250 x (100 +400) = 250 x 500 = 125,000
