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 $32,000$ units and a standard deviation of $7,000$ units. GammaFlu's contract manufacturer charges

$$15$ per unit ordered.

Suppose that after receiving its initial order, GammaFlu observes the actual demand and may place a

second rush order to fill any shortages. The contract manufacturer charges $$17$ per unit ordered

during the second order to cover the additional costs of rush shipping and production associated

with this quick response option.

Calculate the increase in optimal expected profits due to the second order opportunity, i$.$e$.$ the

difference in expected profits when two orders are allowed as compared to only one.

Rounding instructions

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

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