This problem seeks to determine the set of flows that minimizes the total cost of satisfying customer demand. The situation you can model in Excel and solve using Solver or LPSolve is depicted below where two plants can deliver to 3 distribution centers and directly to some retailers. The total cost associated with transporting and storing one unit along the arcs is given in the figure along with the capacity of each plant and the demand at each retailer. Notice that this is a balanced problem where total capacity equals total demand.

A. Write out the models using mathematical notation (not just a spreadsheet or the LPSolve model) where you list every decision variable and what they represent as well as every parameter or input and what they mean. Then write the model using mathematical notation:

 

500 500 Plant 1 Plant 2 DC 1 DC 2 3 DC 3 3 2 2 1 Max flow 400 400 LO 350 6 DC 1 01 6 DC 2 DC 3 4 3 3 2 2 4 2 3 Retail 1 Retail 2 Retail 3 Retail 4 C. Assume that there is also a requirement on the maximum allowable flow through each DC's that is given below: Retail 5 250 150 300 200 100 Determine the flows along each arch that satisfy the design requirements at minimum cost. When you record your answer, include not only the flows along each arc but the total cost as well.