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. Show which variables are basic and which are not, at each step. Compute the value of the objective function and decision variables at optimality:

Maximize Z=12x1 + 18x2
Subject to 6x1 + 5x2 < 60

x1 + 3x2 < 15
x1 < 9
x2 < 4
x1, x2 > 0

(a) It has unique optimal solution
(b) it has alternate optima
(c) it is infeasible
(d) it is unbounded