Once production is under way the marginal net revenue

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required to initiate the production of the airplanes for each customer. Once production is under way, the marginal net revenue (which is the purchase price minus the marginal production cost) from each airplane produced is shown in the second row. Third row gives the percentage of the available production capacity that would be used for each airplane produced. The last row indicates the maximum number of airplanes requested by each customer (but less will be accepted). Customer 1 2 3 Start-up cost $3 million $2 million 0 Marginal net revenue $2 million $3 million $0.8 million Capacity used per plane 20% 40% 20% Maximum order 3 planes 2 planes 5 planes Fly-Right now wants to determine how many airplanes to produce for each customer (if any) to maximize the company’s total profit (total net revenue minus start-up costs). a). Formulate a model as a mixed integer programming model. b). Solve the model by using Excel solver. Question 2 (20 marks): The integer programming can be applied to model some logics. You are asked to formulate the below logics as integer programming constraints: Assumption : The decision variables below are binary integer variables. a). Type A and B cannot be selected at the same time b). If A is selected, at least one of B and C has to be selected. c). If A is not selected, both B and C have to be selected. d). B is selected if and only of D is selected.
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Question 3 (20 marks): Suppose that a mathematical model fits linear programming except for the restriction that |x 1 – x 2 | = 0 or, 3 or, 6. Show how to reformulate this restriction to fit MIP model. Question 4 (30 marks): Consider the following IP problem: Maximize Z = 220x 1 + 80x 2 Subject to: 5x 1 + 2x 2 16 2x 1 x 2 4 –x 1 + 2x 2 4 x 1 , x 2 0 x 1 , x 2 are integers. Use the branch-and-bound algorithm to solve the problem by hand.
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