The owner of a chain of three grocery stores has purchased five crates of fresh strawberries. The estimated probability distribution of potential sales of the strawberries before spoilage differs among the three stores. Therefore, the owner wants to know how to allocate five crates to the three stores to maximize expected profit. For administrative reasons, the owner does not wish to split crates between stores. However, he is willing to distribute no crates to any of his store. The following table gives the estimated expected profit at each store when it is allocated various numbers of crates: 1) Formulate a dynamic optimization problem by identifying explicitly the problem's: i. Decision stages, ii. Decision variables, iii. State variables, iv. State-transition functions, v. Constraints, and vi. Objective-contribution functions. 2) Use dynamic programming algorithm to determine how many of the five crates should be assigned to each of the three stores to maximize the total expected profit