Question

Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit realized from renting out x apartments is given by the following equation in dollars. P(x) = -10x2 + 1,800x - 56,000 (a) How many units should be rented out in order to maximize the monthly rental profit? units (b) What is the maximum monthly profit realizable?

Answer 1

To maximize the monthly rental profit at Lynbrook West, 90 units should be rented out, which will yield a maximum monthly profit of $64,000.

Step-by-step explanation:

The profit function for renting out apartments at Lynbrook West is given by P(x) = -10x2 + 1,800x - 56,000.

Part (a)

To maximize the monthly rental profit, we need to find the value of x that gives us the apex of the parabola represented by the profit function. This can be done by finding the vertex of the parabola, where the x-coordinate of the vertex (h) is given by the formula h = -b/(2a) for a quadratic equation ax2 + bx + c. In this case, a = -10 and b = 1,800, therefore the number of units to maximize the profit is calculated as:

x = -b/(2a) = -1,800/(2 * -10) = 90 units.

Part (b)

To get the maximum monthly profit, plug the value of x into the profit function:

P(90) = -10(90)2 + 1,800(90) - 56,000 = $64,000.

Therefore, the maximum monthly profit realizable is $64,000.