Question (8) [25] (a) In a balanced transportation problem with m sources and n destinations, how many variables can be treated as basic variables and why? (b) In an integer programming problem, a variable x can take three values only 5,10 or 15 . Write it as a constraint. (c) While solving transportation problem, you can randomly assign any value to one of ui or vj 's. However, irrespective of the values of u and v you have, show that the optimal solution of the transportation problem is unique. (d) Hungarian method suggests covering all zeros using the minimum number of horizontal/vertical lines and subtracting the smallest uncovered element from all the uncovered elements, then adding this value to the elements at the intersection of two lines. What is the rationale behind this step? (e) Why would the solution to an assignment problem by transportation simplex method always degenerate