Decision Analysis & Modeling
1. There is a relationship between the Primal and the Dual problem in Linear Programing Problems. In this context explain the Primal and the Dual Problem and establish the relationship between the two.
2. In Assignment Problems, often we face some additional constraints in the form of prohibited assignments. What do you understand by these prohibited assignments?
3. The owner of Fancy Goods Shop is interested to determine how many advertisements to release in the selected three magazines – A, B, and C. His main purpose is to advertise in such a way that total exposure to principal, buyers of his goods is maximised. Percentage of readers for each magazine is known. Exposure in any particular magazine is the number of advertisements released multiplied by the number of principal buyers. The following date is available:
| Magazines | |||
| Particulars | A | B | C |
| Readers | 1.0 lakh | 0.6 lakh | 0.4 lakh |
| Principal Buyers | 20% | 15% | 8% |
| Cost per Advertisement | 8,000 | 6,000 | 5,000 |
The budgeted amount is at the most Rs.1.0 lakh for the advertisements. The owner has already decided that magazine A should have no more than 15 advertisements and that B and C each at least 8 advertisements.
a. Identify the decision variables.
b. Formulate the problem as a Linear Programming Problem.