1. Perform a sensitivity analysis of the Midwestern Hardware scenario (Problem 15). Find the optimal order quantity and optimal expected profit for probabilities of a harsh winter ranging from 0.2 to 0.8 in increments of 0.2. Plot optimal expected profit as a function of the probability of a harsh winter. 2. Dean Kuroff started a business of rehabbing old homes. He recently purchased a circa-1800 Victorian mansion and converted it into a three-family residence. Recently, one of his tenants complained that the refrigerator was not working properly. Since Dean’s cash flow was not extensive, he was not excited about purchasing a new refrigerator. He is considering two other options: purchase a used refrigerator or repair the current unit. He can purchase a new one for $400, and it will easily last three years. If he repairs the current one, he estimates a repair cost of $150, but he also believes that there is only a 30% chance that it will last a full three years and he will end up purchasing a new one anyway. If he buys a used refrigerator for $200, he estimates that there is a 0.6 probability that it will last at least three years. If it breaks down, he will still have the option of repairing it for $150 or buying a new one. Develop a decision tree for this situation and determine Dean’s optimal strategy.