Question 3 Consider the following problem: wheats are shipped from two plants (Plant 1 and Plant 2 in the graph) to either a warehouse (Warehouse) or two distribution centers (Distribution center 1 and Distribution center 2) and then on to the two end markets (Market 1 and Market 2). Warehouse Distribution center 1 $8 Plant 1 $6 $15 Market 1 250 6 200 $6 $10 $9 $15 $2 $7 $14 450 2 500 $17 Plant 2 S4 Market 2 5 Distribution center 2 The production rates are 250 and 450 units per month for Plants 1 and 2 respectively. The demands of the two markets are 200 and 500 units per month respectively. The costs of shipping one unit of wheats over those arcs are shown adjacent to the corresponding arcs in the network. (1) Formulate the LP problem to minimize the total shipping cost per month. You need to clearly define all the decision variables and explain the physical meanings of the objective function and all the constraints. You do NOT need to solve it. (2) Consider the raw wheats are shipped from a farm (Farm in the graph below) to the two plants. An end user (End user in the graph below) purchases all the wheats in the markets. Now, the above network consists of only one origin and one destination. The costs of shipping one unit of raw wheats from the farm to Plant 1 and Plant 2 are $5 and $6 respectively. The costs of shipping one unit of wheats from Market 1 and Market 2 to the end user are $8 and $6 respectively. The revised network is shown below. Find out the shortest path to ship one unit of wheats from the farm to the end user using Dijkstras Algorithm. You need to present the solution process in the Table format (Note that the number of iterations listed in the empty table in the Answer Sheet might not be the same as that in the optimal solution). Warehouse Distribution center 1 S8 Plant 1 $6 3 $15 Market 1 S5 6 $6 S8 $10 Farm End user S9 $15 0 8 S2 S7 $14 $6 7 S6 $17 Plant 2 $4 Market 2 5 Distribution center 2 Iteration 0 1 2 3 4 5 6 7 8 Initial 1 2 3 5 6 7 S