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midterm1_3133_sol

midterm1_3133_sol - Part 1 True or False(30 Mark whether...

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Part 1 - True or False (30%) Mark whether each of the following statements is true or false. No explanation required. The extreme points of the feasible region of an LP are the points on the boundary or perimeter of the region. TRUE FALSE In order for a problem to be correctly modeled as an LP, decision variables must be allowed to be fractional. TRUE FALSE If an LP has two or more optimal solutions, it has infinitely many optimal solutions. TRUE FALSE For the remaining statements, consider an LP max n j =1 c j x j s.t. n j =1 a ij x j b i , i = 1 , . . . , m x j 0 , j = 1 , . . . , n . Suppose x * is optimal for this LP. Any dual feasible solution y satisfies m i =1 b i y i n j =1 c j x * j . TRUE FALSE Any dual optimal solution y * satisfies m i =1 b i y * i n j =1 c j x * j . TRUE FALSE If x * j > 0, any dual optimal solution y * satisfies m i =1 a ij y * i > c j . TRUE FALSE

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Part 2 - Modeling (30%) You are a mutual fund manager, and you must decide how much to invest in three different stocks for the upcoming year. You have the following information available:
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