A car rental agency rents 190 cars per day at a rate of $20 per day. For each $1

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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.