assignment13_ProblemSet

# assignment13_ProblemSet - ORIE 3300/5300 Individual work...

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ORIE 3300/5300 ASSIGNMENT 13 Fall 2008 Individual work. Not to be graded. 1. Consider the following integer program: maximize x 1 + 3 x 2 subject to 2 x 1 + 5 x 2 9 x 1 , x 2 0 , integer . Solve this problem by branch and bound by starting from an optimal tableau for the initial linear programming relaxation, and then using the dual simplex method to solve the linear programming relaxation of each subproblem obtained by adding the extra constraint deﬁning the branch. 2. The diet problem can be written as min c T x,Ax b,x 0, where x j is the amount of food j to be purchased at a unit cost of c j > 0, a ij is the amount of nutrient i provided by each unit of food j , and b i is the daily requirement of nutrient i . After adding surplus variables t and putting into standard equality form, this becomes max( - c ) T x,Ax - t = b,x 0 ,t 0. Show that the initial basis consisting of all the surplus variables is dual-feasible, so that this problem is ideal for solution by the dual simplex method. 3. This exercise illustrates the connection between the dual simplex method

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assignment13_ProblemSet - ORIE 3300/5300 Individual work...

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