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a car rental company has 396 cars on their lot. they can rent all 396 cars at a rate of $44 per day. they determine that for every $1 increase in the rental cost, they will rent 3 fewer cars. find the car rental rate that will maximize daily revenue for the company.

Answer :

Final answer:

To find the car rental rate that will maximize daily revenue for the company, we need to determine the relationship between the rental cost and the number of cars rented. We can set up an equation and take the derivative to find the value of x that maximizes daily revenue.

Explanation:

To find the car rental rate that will maximize daily revenue for the company, we need to determine the relationship between the rental cost and the number of cars rented. We know that for every $1 increase in the rental cost, 3 fewer cars are rented. So, we can set up an equation:

Rental Cost = $44 + $1(x)

Number of Cars Rented = 396 - 3x

Next, we can calculate the daily revenue by multiplying the rental cost by the number of cars rented:

Daily Revenue = (Rental Cost)(Number of Cars Rented)

To find the car rental rate that maximizes daily revenue, we can take the derivative of the daily revenue function with respect to x and set it equal to zero:

Daily Revenue' = 0

Solving for x will give us the value of x (the number of $1 increases in the rental cost) that maximizes daily revenue. We can then substitute this value back into the rental cost equation to find the car rental rate that will maximize the daily revenue for the company.

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