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Lecture - Sept 11.doc

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University of Toronto Scarborough
Management (MGO)
Vinh Quan

MGTC74 Analysis for Decision Making Lecture 01 Chapter 2 – LP Model Formulation & Solution Basic components of linear programming (LP) model: 1) Define decision variables—variables that describes the decisions to be made 2) State objective function—in LP model decision maker will want to maximize (e.g., profit, output, revenue) or minimize (cost, risk) some function of decision variables 3) Specify constraints 4) Sign restrictions or variables—in general we can have x≥0, x≤0, x unrestricted in sign • if x1,x2must be integer, then we have an integer programming problem 2 • if either objective function or any of the constraints is nonlinear e.g., 3x + 21 then w2 have nonlinear programming problem Example – Production Planning 1) x =1# of soldiers to make each week x = # of trains to make each week 2 2) objective is to maximize profits Profit = (27x +121x ) –2(10x + 91 +14x 2 10x 1 = 3x +22x 1 2 3) constraint 1  no more than 100 hrs finishing time used finish time soldier + finish time trains ≤ 100hr  2x + 1x 1100 2 constraint 2  no more than 80hrs carpentry time used 1x 1 1x ≤82 constraint 3  at most 40 soldiers can be sold x 1 40 4) cannot produce negative # of soldiers/trains so x ,x > 1 2 Final LP model Max z = 3x 1 2x 2 2x1+ 1x ≤200 (finishing) 1x1+ 1x ≤20 (carpentry) x1< 40 (soldier demand) x , x > 0 1 2 1 Example – Production Planning For every gallon A
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