Suppose lower- and upper-bounded simplex Algorithm 5D is being applied to a problem with objective function max 3x1 - 4x2 + x3 - 4x4 + 10x5 3 main constraints, and bounds 0 … xj … 5 j = 1,c, 5 For each of the following current basic solutions x and corresponding simplex directions x, determine whether the appropriate move of{x is improving. Also compute the maximum step l that could be applied without losing feasibility and the basis status of variables that would result after such a step. Take the current basic variables to be those strictly between lower and upper bounds.

(a) x = 12, 2, 4, 0, 52 , x = 11, -1, 0, 0, 12 for x5

(b) x = 15, 0, 2, 3, 22,

x = a0, 1, 1 10

, -

1 5

, 1 3

b for x2

(c) x = 10, 1, 0, 4, 22, x = a0, 0, 1, -

2 5

, 2 5

b for x3

(d) x = 15, 5, 1, 3, 1, 2, x = 11, 0, 0, 4, 12 for x1