Consider a retailer that has 5 stores around the US. Assume that this retailer sells only one type of product in its stores. Currently the retailer has 2 warehouses in the east and west of the US. Warehouses supply the needs of the stores.

Figure below illustrates the store and warehouse locations. The blue circles represent the store locations, and the green squares represent the current warehouse locations.

Each store has a known demand, and each warehouse has a limited supply capacity. Table below represents supply capacities, demands, and the cost of supplying a unit of product from each warehouse to each store.

	Store
Warehouse	A	B	C	D	E	Supply
1	3	4	7	20	16	250
2	14	15	17	6	3	400
Demand	102	124	114	200	101

a) Formulate a transportation optimization problem to determine the number of products that should be sent from each warehouse to each store. Clearly specify the decision variables, objective function, and constraints, and write a mathematical model that aims to minimize the transportation costs.

b) Use Excel to solve the optimization model. How many products are shipped from warehouse 2 to customer C? What is the minimum cost of transportation for this problem?

c) Write an additional constraint for the model to ensure that the number of products that are shipped from warehouse 1 to store A is at most 80. Add this new constraint to Excel and resolve the problem. Compare the total transportation cost with the cost that you found in part b. How much does the total transportation costs decrease/increase after adding this new constraint?