A Manufacturing company is planning to produce daily at least 2000 units on three machines. The...
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A Manufacturing company is planning to produce daily at least 2000 units on three machines. The minimum lot size on any machine is 600 units (i.e. the production quantity in a used machine should be more than 600 units). Note that, if a machine is not used, the quantity will be of course 0. The following table gives the pertinent data of the situation. Machine 1 2 3 Setup-cost 300 100 200 Production cost/unit 3 4 5 Daily capacity (units) 1000 800 1200 The company want to know the adequate quantity of units produced on each machine. Write here a formulation (as applied in Lingo) of this problem as a mixed ILP (define precisely the used decision variables) Find the optimum solution using Lingo Software. 2.2) To reduce fixed cost, the company decide that at most two machines should be used for production. Write here the added constraint and find the new optimum solution Page 1/3 1.6) Suppose that the requirement according to Calcium is changed from 14 to 12 (RHS of the first constraint will be 12). Using sensitivity analysis, how will this affect the total cost? Explain Problem 3 (6 pts) Let us consider the following modified 0-1 Knapsack problem. Max 2 X1 +3 X2 + 4 X3 Subject to: 4 X1 +5X2+3 X3 ≤6 X1 + X3≤1 Where: Xi = 1 (i=1, 2, 3) if item i is selected in the knapsack, Xi = 0 otherwise 3.1) Which is the maximum capacity of the knapsack? 3.2) Which item has the weakest value? - 3.3) Gives a possible meaning of the second constraint: X1 + X3 <1? 3.4) Apply Branch and Bound method to solve this problem as a succession of LP problem. Presents all possible branches, write the constraints that have been added at each branch and the state of the obtained solution at each node. A Manufacturing company is planning to produce daily at least 2000 units on three machines. The minimum lot size on any machine is 600 units (i.e. the production quantity in a used machine should be more than 600 units). Note that, if a machine is not used, the quantity will be of course 0. The following table gives the pertinent data of the situation. Machine 1 2 3 Setup-cost 300 100 200 Production cost/unit 3 4 5 Daily capacity (units) 1000 800 1200 The company want to know the adequate quantity of units produced on each machine. Write here a formulation (as applied in Lingo) of this problem as a mixed ILP (define precisely the used decision variables) Find the optimum solution using Lingo Software. 2.2) To reduce fixed cost, the company decide that at most two machines should be used for production. Write here the added constraint and find the new optimum solution Page 1/3 1.6) Suppose that the requirement according to Calcium is changed from 14 to 12 (RHS of the first constraint will be 12). Using sensitivity analysis, how will this affect the total cost? Explain Problem 3 (6 pts) Let us consider the following modified 0-1 Knapsack problem. Max 2 X1 +3 X2 + 4 X3 Subject to: 4 X1 +5X2+3 X3 ≤6 X1 + X3≤1 Where: Xi = 1 (i=1, 2, 3) if item i is selected in the knapsack, Xi = 0 otherwise 3.1) Which is the maximum capacity of the knapsack? 3.2) Which item has the weakest value? - 3.3) Gives a possible meaning of the second constraint: X1 + X3 <1? 3.4) Apply Branch and Bound method to solve this problem as a succession of LP problem. Presents all possible branches, write the constraints that have been added at each branch and the state of the obtained solution at each node.
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Related Book For
Fundamentals of Financial Accounting
ISBN: 978-0078025914
5th edition
Authors: Fred Phillips, Robert Libby, Patricia Libby
Posted Date:
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