Problem 3. A gourmet store sells a perishable delicacy fish, which is brought fresh daily from fishermen just prior to the start of the business day. Unsold fish must be disposed of at the end of the business day. One pound of fish costs the store $28.50 per pound, and sells for $150 per pound. The store sells daily leftover fish to a cat food company at $20 per pound, but there is a transportation cost of $11.40 per pound of unsold inventory. The store estimates that daily demand follows a continuous uniform distribution between 51 and 250 pounds (inclusive) of fish per day, that is, the probability of any quantity of fish, Q, between 51 pounds and 250 pounds is f(Q) = 1/200, and the corresponding cdf is F(Q) = (Q - 50)/ 200 for Q in the same range. Answer the following questions: 3.1) (5 points) Write down the model name and list all the parameters of the problem and their numerical values. 3.2) (10 points) What is the optimal quantity of fish (rounded off to the nearest pound, if not integer) the store should stock each business day? 3.3) (10 points) If the daily demand actually has a normal distribution with mean 150 and standard deviation 20, what is the optimal quantity of fish (rounded off to the nearest pound) the store should stock each business day