An apartment block has seventy units of accommodation. It is estimated that it is possible to let them all if the rent is $2,000 per month, and for each $100 per month the rent is increased there would be one unit vacant.
LG, the manager of the block, finds that a vacant unit costs $100 per month to maintain whereas an occupied one costs $300.
a. If profit from the lettings is measured as revenue minus maintenance costs, find an expression for profit in terms of the number of units let.
b. What rent should LG charge to maximize profit?