Problema Solution
When priced at $30, a toy has monthly sale of 4000 units. For each $1 increase in price, sells will decrease by 100 units. Find the maximum total revenue possible.
Answer provided by our tutors
Let 'x' represent the price after increase then:
Sales:
S = 4000-100(x-30)
S= 7000-100x
So the revenue R is:
R = x*S
R = x(7000-100x)
R = 7000x - 100x^2
We use derivatives to find the maximum:
R'= 7000 - 200x
When x = 35, R'=0, that is, revenue is maximum.
So, the price that will maximize total revenue is $35.00.