Sport Tee Corporation manufactures T$-$shirts bearing the logos of

professional baseball and football teams. The wholesale market for

sport T$-$shirts is perfectly competitive. The manager forecasts the

wholesale price of T$-$shirts next year to be $$7\mathrm{.}00.$ The firm's estimated

marginal cost is

$SMC=12-0\mathrm{.}005Q+0\mathrm{.}0000008Q^2$

where $Q$ is the number of T$-$shirts produced and sold each month.

Sport Tee Corporation will have a fixed cost of $$2,000$ per month.

a$.$ What is the Average variable cost function for Sport Tee?

b$.$ To maximize profit how many T$-$shirts should be produced and

sold each month?

c$.$ At the profit$-$maximizing level of output, what is the total

revenue?

d$.$ What is the monthly profit?