High School

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A car rental company has 444 cars on their lot. They can rent all 444 cars at a rate of $76 per day. They have determined that for every $4 increase in the rental cost, they will rent 3 fewer cars.

Find the car rental rate that will maximize revenue for the company.

Answer :

Answer:

Car rental rate that maximizes revenue is either $332 or $336 per day

Explanation:

The formula for revenue can be stated as: [tex]R = (76+4x)*(444-3x)[/tex], where x is the amount of $4 increases that are going to be applied.

The first part of the equation [tex](76+4x)[/tex] refers to the car rental rate and the second part of the equation [tex](444-3x)[/tex] refers to the cars that are going to be rented.

By elaborating on the formula you have that [tex]R = 33,744 + 1,548x - 12x^{2}[/tex] which can then be simplified into [tex]R = 2812 + 129x - x^{2}[/tex].

After this, you apply the max value function for a quadratic function: [tex]x = -\frac{b}{2a}[/tex], where we have that b is 129 and a is -1.

Then you get that x must be 64.5. In this situation where it is specified that increases can only increase in $4 amounts, I assume that the x must be rounded. Then your x value for maximum revenue is either 64 or 65.

When you apply x=64 or 65 to the car rental rate function, you have that the rate must be either $332 or $336.

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Rewritten by : Barada