The Charm City Utilities Inc. supplies natural gas to customers in three areas. The company purchases natural gas from four companies: A, B, C and D. Demand forecasts from the three areas, supply from the four companies, and the distribution costs per unit (in thousands of dollars) are as follows:

                                              To Area (Cost in Dollars)          

                                                1          2          3          Supply

             ________________________________________________________

                                    A         11        18        15        1000

            From                B         12         14        16        800

                                    C         10          16          18          600

                                    D         8          14        20        500

            ________________________________________________________

            Demand                     800       1000     1000      

(a) Formulate a linear programming problem to minimize total cost for this transportation problem by defining the decision variables, objective function, and all the constraints.

(b) Solve the linear programming formulation from part (a) by using either Excel or QM for Windows. Find and interpret the optimal solution and optimal value. Please also include the computer output with your submission.

The following questions are mathematical modeling questions. Please answer by defining decision variables, objective function, and all the constraints. Write all details of the formulation. Please do NOT solve the problems after formulating.