Goop Incorporated needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be normally distributed with a mean of $200$ gallons and a standard deviation of $100$ gallons. Goop sells the polymer for $$27$ per gallon. Goop purchases raw material for $$7$ per gallon and must spend $$13$ per gallon to dispose of all unused raw material due to government regulations. $($One gallon of raw material yields one gallon of polymer.$)$ If demand is more than Goop can make, then Goop sells only what it has made and the rest of the demand is lost. Use Table $13\mathrm{.}4.$