Solve the following linear program using the simplex method. Explain each simplex pivot by showing a complete basis representation or simplex tableau for each extreme point visited. Compute the value of the objective function and decision variables at optimality, and indicate which statement best describes the solution and why:
Minimize Z = 7x1 – 5x2
Subject to: 2x1 – x2 ≥ 4
10x1 + 3x2 ≤ 30
x1 + 2x2 ≥ 10
x1, x2 ≥ 0
(a) this linear program has a unique optimal solution
(b) this linear program has alternate optima
(c) this linear program is infeasible
(d) this linear program is unbounded
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