Recall from Section 3.3 that for some LPs, there exist points in the feasible region for which z assumes arbitrarily large (in max problems) or arbitrarily small (in min problems)

values. When this situation occurs, we say that LP is unbounded. In this section, we show

how the simplex algorithm can be used to determine whether an LP is unbounded.
Breadco Bakeries bakes two kinds of bread: French and sourdough. Each loaf of French bread can be sold for 36¢, and each loaf of sourdough bread for 30¢. A loaf of French bread requires 1 yeast packet and 6 oz of flour; sourdough requires 1 yeast packet and 5 oz of flour. At present, Breadco has 5 yeast packets and 10 oz of flour. Additional yeast packets can be purchased at 3¢ each, and additional flour at 4¢/oz. Formulate and solve an LP that can be used to maximize Breadco’s profits (= revenues - costs).

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TABLE 19 Initial Tableau for Breadco Z %3 X4 S $2 rhs 1 -36 -30 3 0 1 1 -1 0 (6) 0 1 5 0-1 01 401 00 05 10 Basic Variable z = 0 $1 = 5 $2=10 Ratio 5 nim 10 5186