# P(x) = -11x^2+1830x-34000 (a) What is the actual profit realized from renting the 41st unit, assuming that 40 units have already been rented?

Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting x apartments is represented by the following function.
$$\displaystyle{P}{\left({x}\right)}=-{11}{x}^{{2}}+{1830}{x}-{34000}$$
(a) What is the actual profit realized from renting the 41st unit, assuming that 40 units have already been rented?

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SoosteethicU
Step 1
Consider the given equation for the monthly benefit by renting x apartments:
$$\displaystyle{P}{\left({x}\right)}=-{11}{x}^{{2}}+{1830}{x}-{34000}$$
Step 2
Now calculate the profit by renting 40 apartments:
$$\displaystyle{P}{\left({40}\right)}=-{11}\cdot{40}^{{2}}+{1830}\cdot{40}-{34000}$$
=-17600+73200-34000
=21600
Step 3
Also calculate the profit by renting 41 apartments:
$$\displaystyle{P}{\left({41}\right)}=-{11}\cdot{41}^{{2}}+{1830}\cdot{41}-{34000}$$
=-18497+75030-34000
=22539
Step 4
Therefore,actual benefit realized by renting 41st apartment is calculate as follows:
$$\displaystyle\ \text{ Profit }\ ={P}{\left({41}\right)}-{P}{\left({40}\right)}$$
=22539-21600
=939