(From Hillier and Lieberman, Section 3.5 Problem 3) The production manager of an

Question

(From Hillier and Lieberman, Section 3.5 Problem 3) The production manager of an automotive Company wants to determine the mix of spare parts to produce in order to maximize total profit. The plant of the company produces three types of spare parts for automobiles. The manufacture of each part requires processing on each of two machines, with the following processing times (in hours) Part Machine 0.02 0.05 0.03 0.02 0.05 0.04 2 And each machine is available 40 hours per month. Each part manufactured will yield a unit profit, for machine A is $50, machine B is $40, and machine C is $30. a) (lpt) Formulate a linear programming model for this problem b) (0.5pt) Display the model on an Excel spreadsheet. c) (1 pt) Use the spreadsheet to check the following solutions: (A, B, C) = (500, 500, 300), (350, 1000, 0),(400, 1000, 0) Which of these solutions are feasible? Which of these feasible solutions has the best value of the objective function? d) (0.5pt) Use the Excel Solver to solve this model e) (1pt) Use Guobi (anlp file) to solve this model

Explanation / Answer

Part A B C Machine-1 0.02 0.03 0.05 Machine-2 0.05 0.02 0.04 Decision variables A B C Machine-1 2000 0 0 Machine-2 0 2000 0 So each box here is a decision variable that how many and which part to be made on which machine Part Profit A 50 B 40 c 30 Objective function Maximize profit 180000 So this profit value for a part*total parts produced and sum of it across all parts(A,B,C) Constraints Machine-1 40

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