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Exam 11: Integer Linear Programming

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Question 31

True/False

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The constraint x₁ - x₂ = 0 implies that if project 1 is selected,project 2 cannot be.

A) True
B) False

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Question 32

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Tom's Tailoring has five idle tailors and four custom garments to make.The estimated time (in hours)it would take each tailor to make each garment is listed below.(An 'X' in the table indicates an unacceptable tailor-garment assignment. ) Formulate and solve an integer program for determining the tailor-garment assignments that minimize the total estimated time spent making the four garments.No tailor is to be assigned more than one garment and each garment is to be worked on by only one tailor.

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Define the decision variables:
x_ij = 1 if ...

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Question 33

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Which of the following is the most useful contribution of integer programming?

The LP Relaxation contains the objective function and constraints of the IP problem,but drops all integer restrictions.

Some linear programming problems have a special structure that guarantees the variables will have integer values.

The 0-1 variables in the fixed cost models correspond to

Market Pulse Research has conducted a study for Lucas Furniture on some designs for a new commercial office desk.Three attributes were found to be most influential in determining which desk is most desirable: number of file drawers,the presence or absence of pullout writing boards,and simulated wood or solid color finish.Listed below are the part-worths for each level of each attribute provided by a sample of 7 potential Lucas customers. Suppose the overall utility (sum of part-worths)of the current favorite commercial office desk is 50 for each customer.What is the product design that will maximize the share of choices for the seven sample participants? Formulate and solve,using Lindo or Excel,this 0 - 1 integer programming problem.

Let x₁ and x₂ be 0 - 1 variables whose values indicate whether projects 1 and 2 are not done or are done.Which answer below indicates that project 2 can be done only if project 1 is done?

The solution to the LP Relaxation of a minimization problem will always be less than or equal to the value of the integer program minimization problem.