# FIGURE 4.28 in Software Integrating Code 39 Extended in Software FIGURE 4.28

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5: Periorbital Rejuvenation
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We can easily nd y s that satisfy the inequalities on the right by simply making them large enough, for example (y1 , y2 , y3 ) = (5, 3, 6). But these particular multipliers would tell us that the optimum solution of the LP is at most 200 5 + 300 3 + 400 6 = 4300, a bound that is far too loose to be of interest. What we want is a bound that is as tight as possible, so we should minimize 200y1 + 300y2 + 400y3 subject to the preceding inequalities. And this is a new linear program! Therefore, nding the set of multipliers that gives the best upper bound on our original LP is tantamount to solving a new LP: min 200y1 + 300y2 + 400y3 y1 + y 3 1 y1 , y 2 , y 3 0 By design, any feasible value of this dual LP is an upper bound on the original primal LP. So if we somehow nd a pair of primal and dual feasible values that are equal, then they must both be optimal. Here is just such a pair: Primal : (x1 , x2 ) = (100, 300); Dual : (y1 , y2 , y3 ) = (0, 5, 1). y2 + y 3 6
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