Question

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 (in dollars) that maximizes the total amount of profit?

Answer 1

Let x be the number of $25 increases. Then the revenue is
(50-x)(800+25x)
The cost is 50(50-x)
profit to be maximized then is
p=(50-x)(800+25x)-50(50-x)