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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