5. Consider the solution space in Figure 3.4, where the simplex algorithm starts at point A.

Determine the entering variable in the first iteration together with its value and the improvement in z for each of the following objective functions:

*

(a) Maximize z = XI - 2X2 + 3X3

(b) Maximize z = 5xI + 2x2 + 4X3

(c) Maximize z = -2XI + 7X2 + 2x3

(d) Maximize z = Xl + X2 + x3