A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately $p=90-0\mathrm{.}2D(D$ is the demand or quantity sold per month and $p$ is the price in dollars$).$ The fixed cost is $$1,500$ per month and the variable cost is $$20$ per unit produced.

a$.$ What is the maximum profit per month for this product?

b$.$ What is the range of profitable demand during a month?

a$.$ The maximum profit per month for this product is $

$($Round to the nearest dollar.$)$