E*  15.8.  A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the following table. 

Hauling cost per ton on site

Pit           1              2              3              price per ton

North    30           60           50           100

South    60           30           40           120

 Susan wishes to determine how much to haul from each pit to each site to minimize the total cost

15.1 We have inserted the symbol E* to the left of each problem (or its parts) where Excel should be used (unless your instructor gives you contrary instructions). An asterisk on the problem number indicates that at least a partial answer is given at the end of the problems. 15.1. Consider the transportation problem having the following data:

Unit cost

Destination         1              2              3              Supply

       1       9              6              8              4

       2       7              12           10           3

       3       6              7              6              2

                                                Demand                                     4              2            3

14.3. Consider a resource-allocation problem having the following data:

  Resource           1 Activity              2              Amount resource available

                A             1                              0              5

                B             0                              1              4

                C             2                              1              9

                D             3                              4              21          

Unit profit           30                           20

The objective is to determine the number of units of each activity to undertake so as to maximize the total profit.

E* (a) Formulate a spreadsheet model for this problem.  (b) Graph the feasible region. Use this graph to identify all the corner points. E* (c) Use the spreadsheet to determine the total profit for each of these corner points. Then use this information to identify an optimal solution.

E* (d) Use the Excel Solver to confirm this optimal solution.  (e) Use the graphical method to confirm this optimal solution