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York University
Administrative Studies
ADMS 3330
Terry Conlin

ADMS 3330 W07 FINAL SOLUTIONS 1a There are 4 changes that must be made to a linear program when it is written in standard form 1 A slacksurplus variable is either added or subtracted from each constraint as followsLESS THANconstraints ADD a slack variable S iGREATER THANconstraintsSUBTRACT a surplus variable S i 2 These new variables are also added to the objective function with a zero costprofit coefficient 3 The inequality signs in the constraints are all changed to4 Each variable in the linear program is written in its own columnSolution MIN 3X 4Y 0S 0S0S12 3 STX 2Y S 8 1X 2Y2S 12 2 2X Y S16 3 X Y01b To plot the first constraint we need to find two points on the constraint line This is done as follows First treat each constraint as an equation not as an inequality Using constraint 1 substitute X0 into the equation and solve for Y02Y 8 2Y8 Y4 This gives the coordinates for the first point X0 Y4 Now substitute Y0 into the constraint and solve for XX20 8 wwwstatsdoesntsuckcomX8 X8 This gives us the coordinates for the second point X8 Y0So far we have CONSTRAINTX Y 04 1 8 0 The same process will now be followed in order to plot the remaining two constraints wwwstatsdoesntsuckcom Constraint 202Y 12 2Y12 Y6 X20 12 X12 We now have CONSTRAINTX Y 04 1 8 0 06 2 12 0wwwstatsdoesntsuckcom
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