Acme Clothing Company is anticipating the upcoming winter season and needs to place an order for boots with its supplier, Boots Unlimited. Acme knows that it can$’$t sell pairs of boots for more than $$54$ and that excess inventory can be dumped at a $50\%$ discount. Boots Unlimited has quoted Acme a $$40$ price for each pair of boots. Acme has forecasted demand for its pairs of boots at $400$ with a normally distributed standard deviation on that forecast of $300$ pairs of boots.