Problema Solution
A car rental agency currently rents 200 cars per day at a rate of $30 per car. Market research indicates for each $1 increase in rate, 5 fewer cars are rented. Find the "optimal" rate. i.e. rate to charge which maximizes daily revenue.
Answer provided by our tutors
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we need an equation to define revenue
'n' represent the number of $1 rental rate increases
total revenue = (200-5n)*(30+n)
which simplifies to
-5n^2 + 50n + 6000
or
-5(n-5)^2 + 6125
we want to minimize "(n-5)^2" by setting it to zero, so we need n=5
30 + 5*1 = 35
the optimal rate to charge is $35