From Hillier and Lieberman Section 35 Problem 3 The producti

(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

Solution

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 <= 40 Total time available for machine -1 So LHS is calculated using sumproduct of parts produced on machine-1 and their respective processing times Machine-2 40 <= 40 Total time available for machine -2 So LHS is calculated using sumproduct of parts produced on machine-2 and their respective processing times So the final solution using solver is Part A - Machine-1 2000 Part B - Machine-2 2000 Total profit 180000 1 2 3 C Part-A 500 350 400 Part-B 500 1000 1000 Part-C 300 0 0 Time on machine-1 10 7 8 Time on machine-2 22 20 20 Profit 54000 57500 60000 So all solutions are feasible point(400,1000,0) gives the best value of profit