a You have a 6 m compartment for storing three items. The volumes needed to store 1 unit of items 1, 2, and 3 are 2 m3, 3 m3 and 3 m), respectively. The probabilistic demand for the items is given as follows: No of units 1 2 Probability of demand Item 1 Item 2 Item 3 0.5 0.3 0.3 0.5 0.4 0.2 0 0.2 0.5 0 0.1 0 3 4 The shortage costs per unit for items 1, 2, and 3 are $8, $10, and $15, respectively. How many units of each item should be held in the compartment? a) Formulate an appropriate DP recursion and boundary conditions. Define the stages, decision variables, and states clearly. b) Solve the problem to determine the optimal solution that yields the minimum expected shortage cost (Solving for the last two stages is sufficient, no need to complete the solution). a You have a 6 m compartment for storing three items. The volumes needed to store 1 unit of items 1, 2, and 3 are 2 m3, 3 m3 and 3 m), respectively. The probabilistic demand for the items is given as follows: No of units 1 2 Probability of demand Item 1 Item 2 Item 3 0.5 0.3 0.3 0.5 0.4 0.2 0 0.2 0.5 0 0.1 0 3 4 The shortage costs per unit for items 1, 2, and 3 are $8, $10, and $15, respectively. How many units of each item should be held in the compartment? a) Formulate an appropriate DP recursion and boundary conditions. Define the stages, decision variables, and states clearly. b) Solve the problem to determine the optimal solution that yields the minimum expected shortage cost (Solving for the last two stages is sufficient, no need to complete the solution)