A buyer for a large department store chain must place orders with an athletic shoe manufacturer six months prior to the time the shoes will be sold in the department stores. The buyer must decide on November $1$ how many pairs of the manufacturer$$s newest model of tennis shoes to order for sale during the coming summer season. Assume that each pair of this new brand of tennis shoes costs the department store chain $$45$ per pair. Furthermore, assume that each pair of these shoes can then be sold to the chain$$s customers for $$70$ per pair. Any pairs of these shoes remaining unsold at the end of the summer season will be sold in a closeout sale next fall for $$25$ each. The probability distribution of consumer demand for these tennis shoes during the coming summer season has been assessed by market research specialists and is provided in the file P$06\_35.$xlsx$.$ Finally, assume that the department store chain must purchase these tennis shoes from the manufacturer in lots of $100$ pairs.

Identify the strategy that maximizes the department store chain$$s expected profit earned by purchasing and subsequently selling pairs of the new tennis shoes.