Reference no: EM13590087

1) 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

2) 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.

(a) Formulate a spreadsheet model for this problem. 

(b) Graph the feasible region. Use this graph to identify all the corner points.

(c) Use the spreadsheet to determine the total profit for each of these corner points. Then use this information to identify an optimal solution. 

(d) Use the Excel Solver to confirm this optimal solution. 

(e) Use the graphical method to confirm this optimal solution