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Mascom MASCOM Orange 15.7K/s ill 110 + 22:44 Assignment - II.... Assignment - 11 INME - 323: Operation Research Submit by 31/07/2020 1. Consider the following problem Maximize z = 2x2 + 3x2 - 5x3 x1 + x2 + x3 = 7 2x, - 5x2 + x3 2 10 *.X2,43 20 Use Big M method to solve the problem. 2. Consider the problem Maximize z = 2x: + 4x2 + 4xy - 3x4 Subject to x1 + x2 + x3 = 4 2x, + 4x, + x = 8 X1 X3 X3, X4 20 Solve the problem with x; and Xa as the staring basic variables and without using any artificial variable. (Hint: X3 and xa plays the role of variables. The main difference is that they have nonzero objective coefficient, which must converted to zero before the starting of the solution) 3. Consider the problem Maximize z = 2x + 5x2 + 3x3 Subject to X1 + 2x2 + x3 = 3 2x, - x2 = 4 X1 X2, X3 20 Solve the problem with x3 as slack variables. Thus, no artificial variable is required in the first constraint. In the second constraint, artificial variable R is required. (Hint: xz and xs plays the role of variables. Solve the problem with X3 and R as the staring variable. 4. Consider the following set of constraints: X1 + x2 + x3 = 7 2x, - 5x2 + x3 = 10 X1 X2 X3 20 Solve the problem using two phase method for each of the following objective functions: (a) Maximize 2 = 2x2 + 3x2 - 5x3 (b) Minimize 2 = 2x2 + 3x2 - 5x3 5. Consider the assignment problem in the Table below: Jobs A B D 1 1 $50 $50 - $20 $30 Workers 2 $70 $40 $20 3 $90 $30 $50 4 $70 $20 $60 $70 Assign the jobs in such a way that the total cost of the jobs is the minimum. Mascom MASCOM Orange 15.7K/s ill 110 + 22:44 Assignment - II.... Assignment - 11 INME - 323: Operation Research Submit by 31/07/2020 1. Consider the following problem Maximize z = 2x2 + 3x2 - 5x3 x1 + x2 + x3 = 7 2x, - 5x2 + x3 2 10 *.X2,43 20 Use Big M method to solve the problem. 2. Consider the problem Maximize z = 2x: + 4x2 + 4xy - 3x4 Subject to x1 + x2 + x3 = 4 2x, + 4x, + x = 8 X1 X3 X3, X4 20 Solve the problem with x; and Xa as the staring basic variables and without using any artificial variable. (Hint: X3 and xa plays the role of variables. The main difference is that they have nonzero objective coefficient, which must converted to zero before the starting of the solution) 3. Consider the problem Maximize z = 2x + 5x2 + 3x3 Subject to X1 + 2x2 + x3 = 3 2x, - x2 = 4 X1 X2, X3 20 Solve the problem with x3 as slack variables. Thus, no artificial variable is required in the first constraint. In the second constraint, artificial variable R is required. (Hint: xz and xs plays the role of variables. Solve the problem with X3 and R as the staring variable. 4. Consider the following set of constraints: X1 + x2 + x3 = 7 2x, - 5x2 + x3 = 10 X1 X2 X3 20 Solve the problem using two phase method for each of the following objective functions: (a) Maximize 2 = 2x2 + 3x2 - 5x3 (b) Minimize 2 = 2x2 + 3x2 - 5x3 5. Consider the assignment problem in the Table below: Jobs A B D 1 1 $50 $50 - $20 $30 Workers 2 $70 $40 $20 3 $90 $30 $50 4 $70 $20 $60 $70 Assign the jobs in such a way that the total cost of the jobs is the minimum