A car rental agency rents 180 cars per day at a rate of 30 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?

Rate = $33

Maximum Income = $5445

Explanation:

Let x be the amount of increase in rental to achieve maximum profit.

So, Rate = (30+x)

When rate increase by x, the quantity decreases by (180 -5x).

Income = (30+x) * (180 - 5x)

Income = 5400 - 150x + 180x - 5x²

Income = -5x² + 30x + 5400

The income will be maximized when derivative of Income is zero.

Taking derivative,

The rate at which cars should be rented to earn maximum income is 30 + 3 = $33 per day per car.

Maximum Income will be,

Rate = 33

Quantity = 180 - 5(3) = 165 cars

Max Income = 33 * 165 = $5445

Rate= $33/day

Maximum Income= $5,445

Explanation:

Rental: (Rx)= (30+x) dollars per day

Number of car rented: N(x) = (180 -5x)

Income

I (x)= (30+x)× (180 -5x)

Open bracket by (30 +x)

30(180-5x)+x(180-5x)

5400-150x+180x-5x²

= 5400+30x-5x²

Therefore the maximum that will be achieved when the derivative of I(x) is zero

dI(x)/dx

30-10x=0

=30/10x

x= 3

For an even dollar rental amount,an increase of $3/days will generate the same income

$30+$3= $33/day

Hence: The rate in which the cars should be rented in order to produce maximum income is $33/day

Maximum Income

180 -(5×3)

=180-15

=165

165×33=$5,445

Maximum Income= $5,445

The maximum income is $5,445

answer; i believe that the correct answer is (an elevator pitch);

answer///a coalition;