11)

Step 1:

Let is the price and is the number of trucks, then

.

And .

Step 2:

Find the profit function.

Profit = Revenue - Costs

.

Step 3:

Find the extreme(maximum) value of profit function by solving .

Therefore, when the truck rental company have a maximum profit.

Solution:

The profit is maximized when per day.

Second method:

11)

Step 1:

Intial rent of the truck is $20/day when 30 trucks are rented.

For every $1 increase in rent of the truck, the number of trucks rented decrease by one.

Let times the rent of the truck is increase then  number of trucks rented decrese by .

And .

Step 2:

Find the profit function.

Profit = Revenue - Costs

\ \