Consider the solution space in Figure 3.16 with the solution starting at the origin A = (0, 0, 0). For each of the objective functions listed below: Select the nonbasic variable that leads to the next simplex corner-point solution, identify the next solution point as A, B, . . ., or J, and determine the associated objective value, z.

(a) Maximize z = x₁ − 2x₂ + 3x₃

(b) Maximize z = 5x₁ + 2x₂ + 4x₃

(c) Maximize z = −2x₁ + 7x₂ + 2x₃

(d) Maximize z = x₁ + x₂ + x₃

FIGURE 3.16

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Components of an LP numerical algorithm Input model Pre-solver Solver Output results