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1. A firm manufactures two products; the net profit on product 1 is Rupees 3 per unit and Rupees 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. (solve with graphical method)
2. Use the graphical method to solve the LPP
Maximize Z = 2X1 + 4X2
Subject to constraints:
X1 + 2X2 ≤ 5
X1 + X2 ≤ 4
And X1, X2 ≥ 0
3. Write the dual of following problems:
- Maximize Z = 7X1 + 5X2
Subject to:
X1 + 2X2 ≤ 6
4X1 + 3X2 ≤ 12
X1, X2 ≥ 0
- Maximize Z= 3X1 + 4X2
Subject to:
5X1 + 4X2 ≤ 200
3X1 + 5X2 ≤ 150
5X1 + 4X2 ≥ 100
8X1 + 4X2 ≥ 80
X1, X2 ≥ 0
4. Determine initial basic feasible solution to the following transportation problem using the north west corner rule.
| D1 | D2 | D3 | D4 | Availability | |
| O1 | 6 | 4 | 1 | 5 | 14 |
| O2 | 8 | 9 | 2 | 7 | 16 |
| O3 | 4 | 3 | 6 | 2 | 5 |
| Requirement | 6 | 10 | 15 | 4 | 35 |
5. Obtain an initial basic feasible solution to the following transportation problem using Vogel’s approximation method.
| D1 | D2 | D3 | D4 | ||
| A | 5 | 1 | 3 | 3 | 34 |
| B | 3 | 3 | 5 | 4 | 15 |
| C | 6 | 4 | 4 | 3 | 12 |
| D | 4 | -1 | 4 | 2 | 19 |
| 21 | 25 | 17 | 17 | 80 |
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