Chapter 9.4, Problem 14E

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).

14. Solve Example 2 in Section 9.2.

EXAMPLE 2 An oil refining company has two refineries that produce three grades of unleaded gasoline. Each day refinery A produces 12,000 gallons of regular, 4000 gallons of premium, and 1000 gallons of super gas, at a cost of $3500. Each day refinery B produces 4000 gallons of regular, 4000 gallons of premium, and 5000 gallons of super gas, at a cost of $3000. An order is received for 48,000 gallons of regular, 32,000 gallons of premium, and 20,000 gallons of super gas. Set up a mathematical problem that determines the number of days each refinery should operate in order to fill the order at the least cost.