Lecture 5

Lecture 5

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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. Non-negativity constraints for all variables. 2. All remaining constraints are expressed as equality constraints. 3. The right hand side vector, b, is non-negative. 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...
View Full Document

Ask a homework question - tutors are online