Page 89 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes 3.7 Review Questions

1. Explain the simplex procedure to solve the Linear Programming Problem.
2. How do you recognize optimality in the simplex method?

3. Can a vector that is inserted at one iteration in simplex method be removed immediately
at the next iteration? When can this occur and when is it impossible?
4. Explain briefly the term 'Artificial' variables.

5. Explain the use of artificial variables in L.P..
6. Maximize: Z = x + x
1 2
Subject to x + 5x  5
1 2
2x + x  4 with x , x non-negative.
1 2 1 2
7. Minimize: Z = 3x + 4x
1 2
Subject to 2x + x  6
1 2
2x + 3x  9
1 2
With, x , x non-negative.
1 2
8. Minimize: Z = x + 2x
1 2
Subject to x + 3x  11
1 2
2x + x  9
1 2
With, x , x non-negative.
1 2
9. Maximize Z = –x – x
1 2
Subject to x + 2x  5000
1 2
5x + 3x  12000
1 2
With, x , x non-negative
1 2
10. Maximize Z = 2x + 3x + 4x
1 2 3
x + x + x  1
1 2 3
x + x + 2x = 2
1 2 3
2x + 2x + x  4
1 2 3
With all variables non-negative

11. Minimize: Z = 14x + 13x + 11x + 13x + 13x + 12x
1 2 3 4 5 6
Subject to x + x + x = 1200
1 2 3
x + x + x = 1000
4 5 6
x + x = 1000
1 4
x + x = 700
2 5
x + x = 500
3 6
With all variables non-negative.

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