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Suppose that we wish to solve

Let c = (4, 3, 0, 0)T , b = (12, 14)T , (A, I₂) = It is easy to see that x = (x₁, x₂, x₃, x₄)T = (0, 0, 12, 14)T satisfies the constraints. Thus, x is a basic feasible solution with basis J = {3, 4} (the third and fourth components of x), whose basic variables are x₃ = 12 and x₄ = 14.

Note that x is not optimal: z(x) = cT x = 0. The optimization procedure constructs a sequence of tables, called simplex tableaus. The first tableau summarizes the data c, b, A′ and the basic variables. The last row is equal to –cT.

Table 1.1. First simplex tableau