Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. p(x)=-12x^2+2160x-59000 To maximize the monthly rental profit, how many units should be rented out? units What is the maximum monthly profit realizable?

To maximize the monthly rental profit, 90 units should be rented out.

The maximum monthly profit realizable is $38,200.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

It's vertex is the point

In which

Where

If a<0, the vertex is a maximum point, that is, the maximum value happens at , and it's value is .

In this question:

Quadratic equation with

To maximize the monthly rental profit, how many units should be rented out?

This is the x-value of the vertex, so:

To maximize the monthly rental profit, 90 units should be rented out.

What is the maximum monthly profit realizable?

This is p(90). So

The maximum monthly profit realizable is $38,200.

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