The Knitting Company $($TKC$)$ is planning production for its four sweater styles that are popular during Christmas. All four styles have demand that is normally distributed. The best$-$selling style has an expected demand of $30,000$ and a standard deviation of $5,000.$ Each of the other three styles has an expected demand of $10,000$ with a standard deviation of $4,000.$ Currently, all sweaters are produced before the start of the season. Production cost is $$20$ per sweater, and they are sold for a wholesale price of $$35.$ Any unsold sweaters at the end of the season are discounted to $$15,$ and they all sell at that price. It costs $$2$ to hold the sweater in inventory for the entire season if it does not sell.