Midterm_ Practice Problems (1).pdf - IE 310: Operations...

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IE310:OperationsResearchPractice Problems_ Midterm1. Consider the following LP:maxZ=10x1+20xx1-2x2-15x1+x21-5x1-3x2≥-45x1,x20(a)IstheLPinstandardform?Ifnot,writethestandardformoftheLP.(b)Drawthefeasibleregion.(c)DeterminetheoptimalsolutiontothisLP,usingwhichevermethodyoufindtheeasiest.2.ConsiderthefollowingLP:maxZ= 4x1+x2-x3x1+ 3x263x1+x2-x39x1, x2, x30(a) Formulate the augmented LP.(b) How many basic variables does this LP have?(c) How many constraints (excluding non-negativity constraints) does the dual LP have?(d) How many basic variables does the dual LP have?(e) Ifx1, x2are basic variables in the above, then what areB,B-1andB-1b?3ConsiderthefollowingLP:minZ= 2x1+ 3x2x1+x25x11x22Show thatx1= 3, x2= 2 is an optimal solution by showing that the objective value of anyfeasible solution is at least 12. (Hint: Duality)221Spring 2019

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