Question

t) A car rental agency rents 210 cars per day at a rate of 27 dollars per day. For each 1 dollar increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income, and what is the maximum income?

Answer 1

$34.5

$5,951.5

Explanation:

P(x)=27+x

Quantity (x)=210-5x

Income(y)=price×quantity

=(27+x)(210-5x)

=5670-135x+210-5x^2

y= -5x^2+75x+5670

dy/dx= -10x+75=0

-10x=-75

x=-75/-10

=7.5

x=7.5

Maximum income=27+x

=27+7.5

=$34.5

Total income=(27+x)(210-5x)

=(27+7.5){210-5(7.5)}

=(34.5)(210-37.5)

=(34.5)(172.5)

=$5,951.25