One month prior to flu season, GammaFlu must decide how many doses of this year's flu vaccine to

order from its contract manufacturer. GammaFlu sells the vaccines for $$22$ per unit. Any unsold

vaccines at the end of flu season can be sold in a secondary market for $$13.$ It costs $$1$ to hold a unit

in inventory through the selling season. Demand is estimated to be normally distributed with a mean

of $50,000$ units and a standard deviation of $7,000$ units. GammaFlu's contract manufacturer charges

$$15$ per unit ordered.

Calculate the optimal expected profit associated with the optimal order quantity.

Rounding instructions

Carry all calculations to at least $3$ decimal places.

Enter your final answer rounded to one decimal place $($nearest tenth$).$