From three warehouses W1, W2, and W3 the stocks are to be transported to four markets M1, M2, and M4. The supplies from warehouses are 300, 200, and 250 tons respectively. Whereas the requirements of markets are 325, 175, 100, 150 tons respectively.
The cost matrix and initial solution is a given in the following table.
| Warehouses | Markets | |||||||
| M1 | M2 | M3 | M4 | |||||
| W1 |
300 |
10 | 10 | 16 | 20 | |||
| W2 | 16 |
175 |
6 |
25 |
17 | 25 | ||
| W3 |
25 |
8 | 21 |
75 |
10 |
150 |
15 | |
Perform the Post Optimality Analysis on the above table and answer the following:
(i)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Is the above solution feasible?
(ii)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Is the solution optimal? Is there more than one solution?
(iii)Â Â Â Â Â Â Â Â Â Â Â Â Is it degenerate?
(iv)Â Â Â Â Â Â Â Â Â Â Â Â Calculate the opportunity cost of transport ting one unit from W1 to M4.
(v)Â Â Â Â Â Â Â Â Â Â Â Â Â Â The manager is forced to transport one unit from W2 to M4, find the rate of increase in the cost per unit.
(vi)Â Â Â Â Â Â Â Â Â Â Â Â If a transport carrier offers 20% discount on route W2 to M4 provided at least 20 units are transported from this route, should the management accept the offer?
(vii)          Due to some problem at W1 its supply is reduced by 2 units. To compensate for the loss it is decided to increase the supply by 2 units from W2. Will such a decision lead to increase the cost? If yes what is the increase/
(viii)        To improve the condition of the market, it is decided to undertake advertising campaign.  However, due to budget constraints only one market can be chosen at present. Decide in which market the advertising campaign should be undertaken?
Is there any solution for above question?