Consider the three-variable linear programming problem shown in Fig. 5.2. (a) Construct a table like Table 5.4,

Question:

Consider the three-variable linear programming problem shown in Fig. 5.2.

(a) Construct a table like Table 5.4, giving the indicating variable for each constraint boundary equation and original constraint.

boundary equation and original constraint.

(b) For the CPF solution (2, 4, 3) and its three adjacent CPF solutions (4, 2, 4), (0, 4, 2), and (2, 4, 0), construct a table like Table 5.5, showing the corresponding defining equations, BF solution, and nonbasic variables.

(c) Use the sets of defining equations from part (b) to demonstrate that (4, 2, 4), (0, 4, 2), and (2, 4, 0) are indeed adjacent to (2, 4, 3), but that none of these three CPF solutions are adjacent to each other. Then use the sets of nonbasic variables from part (b) to demonstrate the same thing.