A car rental agency rents 190 cars per day at a rate of $20 per day. For each $1
ID: 2878959 • Letter: A
Question
A car rental agency rents 190 cars per day at a rate of $20 per day. For each $1 increase in rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What is the maximum income?
A car rental agency rents 190 cars per day at a rate of $20 per day. For each $1 increase in rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What is the maximum income? The rental agency will earn a maximum income of s when it charges s per day.Explanation / Answer
let number of cars rented per day = n , rate per day =p
agency rents 190 cars per day at a rate of $20 per day
For each $1 increase in rate, 5 fewer cars are rented=>
agency rents 185 cars per day at a rate of $21 per day
(p1,n1)=(20,190),(p2,n2)=(21,185)
n-n1=[(n2-n1)/(p2-p1)](p-p1)
n-190=[(185-190)/(21-20)](p-20)
n-190=-5(p-20)
n-190=-5p +100
n =-5p +290
income I =number of cars* rent per car
I=(-5p +290)p
I=(-5p2 +290p)
I=-5(p2 -58p)
I=-5(p2 -58p+(58/2)2-(58/2)2)
I=-5(p2 -58p+(29)2-(29)2)
I=-5(p2 -58p+(29)2)+ 5*(29)2
I=-5(p -29)2+4205
vertex is (29,4205), income cuve is open downwards
so rental agency earns maximum income of 4205 dollars when it charges 29 dollars per day