problem 1)a) describe the role of operations research in decision making?

b) prepare down the limitations of linear programming?

c) Why do we add slack and subtract surplus variables for solving problems by simplex method?

d) Obtain the dual of linear program Max.

Z = 3x₁ + 5x₂ + 7x₃

Subject to: x₁ +x₂+ 3x₃ ≤ 10

4x₁- x₂ +2x₃ ≥ 15

where x₁, x₂ ≥ 0 and x₃ is unrestricted.

e) How does the assignment model form the special case of transportation model?

f) What do you mean by the term Saddle point'?

g) prepare down the typical features of the problems, which are best suited to be solved by Dynamic programming techniques?

h) prepare down the difference between CpM and pERT?

i) What is degeneracy in transportation problems? When does it creep into the solution?

j) What will happen to gain of a player if he plays mixed strategy in a game where saddle point exists.