Problema Solution
When priced at $33 each, a toy has annual sales of 4,500 units. The manufacturer estimates that each $1 increase in cost will decrease sales by 100 units. Find the unit price that will maximize total revenue.
Answer provided by our tutors
Price:
P = x
Sales:
S = 4500-100(x-1) = 4600-100x
The revenue is price multiplies by sales:
R = P*S
R = x(4600-100x)
R = -100x^2 + 4600x
We need to find the value of x that will maximize R:
x = -b/2a, where a = -100, b = 4600
x = -4600/(2*(-100))
x = $23
The price that will maximize total revenue is $23.00 per unit.