Runner$$s World launched a new model of running shoes called $$Nirvana$.$ A pair of $$Nirvana$$ is sold for $$68$ and costs $$30$ to make. If $$Nirvana$$ does not get sold by the end of the season, it is sold to an outlet store for the discounted price of $$25$ per pair. Additionally, the shipping cost to the outlet store for unsold shoes is $$5$ per pair. The demand for $$Nirvana$$ for the season is forecast to be normally distributed with a mean of $920$ and a standard deviation of $160.$ What is the expected sales if the company makes $1100$ pairs of $$Nirvana$$ shoes for the season? What is the expected leftover inventory if the company makes $1000$ pairs of $$Nirvana$$ shoes for the season? What is the fill rate when the company makes $1000$ pairs of $$Nirvana$?$ What is the optimal $($profit$-$maximizing$)$ production quantity of $$Nirvana$$ for the season? What is the expected profit for Runner$$s World if the company makes $850$ pairs of $$Nirvana$?($Enter only a number, which should be the profit in dollars. E$.$g$.$ if your answer is $$80\mathrm{.}25,$ enter $80\mathrm{.}25.)$ How many pairs of $$Nirvana$$ should Runner$$s World make to achieve a $1\%$ stockout probability? Choose the closest answer. How many pairs of $$Nirvana$$ should Runner$$s World make to achieve $99\%$ fill rate? Choose the closest answer.