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# DOCUMENTS - IEOR 4403 Adv Engineering Corporate Economics...

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IEOR 4403 Adv Engineering & Corporate Economics Professor Ali Sadighian Fall 2011 Homework #4 Due in class on December 11th, 2011 Problem 1 a. All linear programs must have (check all that necessarily apply): 1) Objective function 2) Dual variables 3) Optimal solution 4) Decision variables 5) Constraints 6) Active constraints b. Answer Yes or No (all questions below relate to linear programs): 1) A feasible solution is defined as an assignment of decision variables such that the objective function given by that assignment can be feasibly higher or lower than the objective value given by other assignments. 2) An optimal solution may not exist. 3) The shadow price of an active constraint is zero. 4) Simplex algorithm is a versatile computational method that solves linear programs, integer programs and mixed integer programs. 5) An optimal solution is not necessarily feasible because in some cases it does not satisfy the definition from part (a) above. 6) The following is NOT a linear program: ( ) ( ) c. Answer in 100 or less words (longer answers will be penalized). In many decision environments the total number of major projects to be considered is ten or fewer. Thus, enumeration of all combinations would be feasible, since there would be 2 10 = 1,024 or fewer combinations. In such a case, would it make sense to use a mathematical programming approach? What information would the mathematical programming approach give that is not available from enumeration?

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2 Problem 2 The Italian government is negotiating a restructure of its debt with its bond holders. In
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