hw2.sol - IE 335 Operations Research - Optimization...

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IE 335 Operations Research - Optimization Solutions to Homework 2 Spring 2012 Problem 7 (a) We define the decision variables C and D such that C = number of chairs D = number of desks Now, we can define the optimization model as follows: maximize 40 D + 25 C subject to C 2 D 4 D + 3 C 20 C,D 0 and integer (b) The optimal solution is C = 4 and D = 2 thus resulting in a profit of 40 × 2 + 25 × 4 = 180 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Number of chairs (C) Number of desks (D) Simplex Company Graphical Solution 4D+3C = 20 C =2D Optimal Solution C,D integer Feasible Set 40D + 25C = 60 40D + 25C = 120 40D + 25C = 180 (c) Yes. The optimal value contour intersects the feasible set at exactly one point, i.e. (4,2) and therefore we have a unique optimal solution. See the graph below. (d) There are several ways to render this problem infeasible. One way would be to add the following constraint: 1
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D 3 Hence the model is infeasible since there are no points which satisfy all the constraints. (e) For now, we assume fractional solutions are acceptable, and so we ignore any integrality constraints. Therefore, we can formulate and solve the model as a linear program (LP) instead of a mixed-integer-program (MIP). The GAMS LST file has been included which verifies the optimal values for the objective function, objval = 180, C = 4 and D = 2. 2
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GAMS Rev 230 WEX-VIS 23.0.2 x86/MS Windows 09/05/11 18:26:11 Page 1 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m C o m p i l a t i o n 1 variables 2 objval "Objective function value" 3 C "# manufactured chairs" 4 D "# manufactured desks"; 5 6 free variables 7 objval; 8 9 positive variables 10 C, D; 11 12 equations 13 obj "Total profit" 14 marketing "Marketing restrictions" 15 cap_wood "Available units of wood"; 16
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This note was uploaded on 02/22/2012 for the course IE 335 taught by Professor Jean-philippe,r during the Spring '08 term at Purdue University-West Lafayette.

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hw2.sol - IE 335 Operations Research - Optimization...

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