(Solved): The Supermarket Store is about to place an order for Halloween candy. One best-selling brand of can ...

The Supermarket Store is about to place an order for Halloween candy. One best-selling brand of candy can be purchased for \( \mathrm{c}=\$ 4.50 \) per box before and up to Halloween. After Halloween, all the remaining candy can be marked down and sold for \( \mathrm{v}=\$ 1.00 \) per box. Assume that the unit loss in goodwill stemming from customers whose demand is not satisfied is \( \mathrm{B}=\$ 0.50 \). Through an assessment of the consumer market for the candy, the store manager, not surprisingly, finds that market demand is sales price dependent and uncertain. For three potential sales prices, the manager estimated the following empirical probability demand distributions: You are required to: 1. Determine the optimal capacity ( \( \mathrm{Q}^{*} \) ), associated expected profit and expected shortage for each sales price. Showing all work, present your results by completing the following table: \begin{tabular}{|l|c|c|c|} \hline Sales Price & \begin{tabular}{c} Optimal Capacity \\ \( \left(\mathbf{Q}^{*}\right) \) in units \end{tabular} & \begin{tabular}{c} Expected \\ Shortage ES(Q*) \\ in boxes \end{tabular} & \begin{tabular}{c} Expected Profit \\ E[ \( \Pi\left(Q^{*}\right) \) in \$ \end{tabular} \\ \hline\( \$ 5 \) & & & \\ \hline\( \$ 6 \) & & & \\ \hline\( \$ 7 \) & & & \\ \hline \end{tabular} 2. Based on the results in the table, answer the following questions: - Which sales price should be chosen if the manager wants to minimize the expected shortage? \( \$ \) - Which sales price should be chosen if the manager wants to maximize the expected profit? \( \$ \)