Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by To maximize the monthly rental profit, how many units should be rented out? What is the maximum monthly profit realizable?
A) 88 units are rented and the maximum monthly profit realizable is $23,720
B) 22 units are rented and the maximum monthly profit realizable is $47,440
C) 88 units are rented and the maximum monthly profit realizable ix $11,860
D) 88 units are rented and the maximum monthly profit realizable is $47,440
E) 44 units are rented and the maximum monthly profit realizable is $47,440

Question

Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by  To maximize the monthly rental profit, how many units should be rented out? What is the maximum monthly profit realizable?
A) 88 units are rented and the maximum monthly profit realizable is $23,720 
B) 22 units are rented and the maximum monthly profit realizable is $47,440 
C) 88 units are rented and the maximum monthly profit realizable ix $11,860 
D) 88 units are rented and the maximum monthly profit realizable is $47,440 
E) 44 units are rented and the maximum monthly profit realizable is $47,440

Quizplus · Accepted Answer

We need to maximize the monthly rental profit, which is given by the function:

P(x) = x(2000 - 10x)

where x is the number of units rented.

To find the maximum profit, we need to find the vertex of the parabola that represents this function. We can do this by finding the x-coordinate of the vertex:

x = -b/2a

where a = -10 and b = 2000

x = -2000/(2*(-10)) = 100

This means that the maximum profit is obtained when 100/2 = 50 two-bedroom units are rented out.

Substituting this value into the profit function, we get:

P(50) = 50(2000 - 10(50)) = $47,440

Therefore, the best choice is D: 88 units are rented and the maximum monthly profit realizable is $47,440.

Lynbrook West, an Apartment Complex, Has 100 Two-Bedroom Units