3. Power PicklesThe is a nutrition company specializing in caffeine-infused pickles. The company has three pickle plants that produce the pickles and four outlet stores that sell them. The company wishes to ship packages of pickles through Its distribution network, from the plants to the stores, at minimum ocet while satisfying constraints on pickle production, store demand, and capacity along shipping arce. The distribution network comprises 11 nodes: the plants (nodes 1-3), the stores (nodes 8-11), and the transshipment nodes (4-7). The below tables indicate the respective supply and demand (in packages of pickles) at the plants and stores Store Plant Supply 9 10 11 Demand 76 95 50 120 80 The below table indicates the per-unit shipping costs of pickle packages (this is available Is a few on the course Blackboard site as prob3_coats. cav). 1 2 3 5 T 8 9 10 11 $1 $10 $2 $10 $2 $10 $10 2 SOONGRANNY $2 $1 $10 $2 $1 $10 $10 $7 $2 $10 $7 $6 11 $2 84 $2 The below table Indicates the maximum shipping capacity along each of the are in Power Pickle's distribution network. A capacity (and east) that is blank Indicates that that are does not exist. (This data is available as a may on the course Blackboard site as prob3.capacities. cor]. [a) Formulate this as a minimum ocet network flow problem. You may assume con- tinuous variables. Label your variables and constraints. (b) Solve this problem wing MATLAB or other software. What is your solution? (e] Comment on the solution. Specifically, are there ares/edges that are maxed out, while others receive little or no flow? What recommendations would you make to Power Pickles management? 1 2 3 4 5 6 7 8 9 10 11 31 29 27 45 34 29 32 29 29 30 44 26 39 31 37 27 40 24 44 87 27 38 27 26 25 25 30 36 31 42 26 43 20 44 41 27 45 27 27 44 43 43 41 41 26 87 44 27 43 10 42 25 38 31 11 $1 38 42 38