Chapter 9.4, Problem 11E

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).

11. Maximize 16x₁ + 10x₂ + 20x₃

subject to     x₁ + x₂ + 3x₃ ≥ 4

2x₁ + x₂ + 2x₃ ≥ 5

and x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0