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SIE340: Deterministic Operations Research Midterm Exam - University Of Arizona

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SIE340: Deterministic Operations Research Midterm Exam - University Of Arizona 1. True or False (10 points, 2 points each question) Please write in the line “T” if the statement is true, or “ ... F” if the statement is false. a) ____ A feasible solution is a solution that satisfies all the constraints. b) ____ A linear function can include the product of two variables, e.g. ?(?$, ?&) = ?$?&. c) ____ A constraint is nonbinding if the left-hand side and right-hand side of the constraint are equal when the optimal values of the variables are plugged in the constraint. d) ____ The set in Figure 1 (below) is convex. Figure 1. The set under study is represented by the gray area. e) ____ For a maximization problem, the optimal objective values for an integer programming problem is less than or equal to the optimal objective value of its LP (linear programming) relaxation.SIE340 Midterm Exam 1 Page 3 of 10 2. LP model and graphical method (30 points: 15 points modeling, 15 points solving) Following the 5 steps introduced in class, model the following problem as a linear program and solve it by the graphical method (a template is provided in Figure 2, next page). LightCo produces two types of lamps (type I and type II) that require metal parts and electrical components. Each lamp type I requires 1 unit of metal part, and 2 units of electrical components, and it can be sold for $1. Each lamp type II requires 3 units of metal parts and 2 units of electrical components, and it can be sold for $2. LightCo has 200 units of metal parts and 300 units of electrical components every day. There is no limit for the demand of lamp I, while the customer is not willing to buy more than 60 lamps of type II every day. The management team wants to maximize the profits of LightCo. 2.1) Please model this problem as an LP (decision variables must be clearly explained) [Show More]

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