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Unformatted text preview: 540:311 DETERMINISTIC MODELS IN OPERATIONS RESEARCH Lecture 6: Chapter 4.1‐4.4 The Simplex Algorithm Class MeeCng: Mon Feb 7th 10:20‐11:40am Prof. W. Art Chaovalitwongse 4.1 – How to Convert an LP to Standard Form Before the simplex algorithm can be used to solve an LP, the
LP must be converted into a problem where all the
constraints are equations and all variables are nonnegative.
We say that a linear program is in standard form if the following
are all true:
1. Nonnegativity constraints for all variables.
2. All remaining constraints are expressed as equality
constraints.
3. The right hand side vector, b, is nonnegative. 4.1 – How to Convert an LP to Standard Form Leather Limited manufactures two types of leather belts: the deluxe model and the regular model. Each type requires 1 square yard of leather. A regular belt requires 1 hour of skilled labor and a deluxe belt requires 2 hours of skilled labor. Each week, 40 square yards of leather and 60 hours of skilled labor are available. Each regular belt contributes $3 proﬁt and each deluxe belt $4. Write an LP to maximize proﬁt. The decision variables are: x1 = number of deluxe belts produced weekly x2 = number of regular belts produced weekly the appropriate LP is: max z = 4x1 + 3x2 s.t. x1 + x2 ≤ 40 (leather constraint) 2x1 + x2 ≤ 60 (labor constraint) x1, x2 ≥ 0 To convert the leather and labor (≤) constraints to equaliWes, we deﬁne for each constraint a slack variable si (si = slack variable for the ith constraint). A slack variable is the amount of the resource unused in the ith constraint. 4.1 – How to Convert an LP to Standard Form The...
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