Problem 3: You are the manager of an apartment complex with 50 units. When you set rent at $800/month, all apartments are rented. As you increase
rent by $25/month, one fewer apartment is rented. Maintenance costs run
$50/month for each occupied unit. What is the rent that maximizes the total
amount of profit?

$475

Step-by-step explanation:

1 Unit = $800, and 50 Units = $800 × 50 = $40,000. Maintenance cost = $50×50 = $2500. Apartment gross income = $40,000-$2,500= $37,500. Increment = $800 + 25 = $825, After increment, one fewer apartment was rented meaning, (50-1) apartment = 49 apartment was rented. After the increment, 49 × 825 = $40,425. Maintenance cost= 49×$50=$2450. After increment, the gross income will be $40,425-$2450= $37,975. Now, the rent that maximises the total amount of rent is the gross income for the new rent - the gross income for the old rent = $37975 - $37,500 = $475.

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