Chapter 9.4, Problem 13E

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).

13. Solve Exercise 2 in Section 9.2.

2. A dog breeder decides to feed his dogs a combination of two dog foods: Pixie Power and Misty Might. He wants the dogs to receive four nutritional factors each month. The amounts of these factors (a, b, c, and d) contained in 1 bag of each dog food are shown in the following chart, together with the total amounts needed.

	a	b	c	d
Pixie Power	3	2	1	2
Misty Might	2	4	3	1
Needed	28	30	20	25

The costs per bag are $50 for Pixie Power and $40 for Misty Might. How many bags of each dog food should be blended to meet the nutritional requirements at the lowest cost? Set this up as a linear programming problem in the following form: Minimize c^Tx subject to Ax ≥ b and x ≥ 0. Do not find the solution.