Chapter 9.4, Problem 12E

Sometimes a minimization problem has inequalities only of the “≥” type. In this case, replace the problem by its dual. (Multiplying the original inequalities by − 1 to reverse their direction will not work, because the basic solution of die initial simplex tableau in this case will be infeasible.) In Exercises 11-14, use the simplex method to solve the dual, and from this solve die original problem (the dual of die dual).

12. Maximize 10x₁ + 14x₂

subject to     x₁ + 2x₂ ≥ 3

2x₁ + x₂ ≥ 4

3x₁ + x₂ ≥ 2

and x₁ ≥ 0, x₂ ≥ 0.