Management And Organizational Behavior

47) Consider the following integer linear programming problem Max Z = 3x 1 + 2x 2 Subject to: 3x 1 + 5x 2 ≤ 30 4x 1 + 2x 2 ≤ 28 x 1 ≤ 8 x 1 , x 2 ≥ 0 and integer The solution to the Linear programming relaxation is: x 1 = 5.714, x 2 = 2.571. What is the optimal solution to the integer linear programming problem? State the optimal values of decision variables and the value of the objective function. Answer: x 1 = 6, x 2 = 2, Z = 22 Diff: 2 Page Ref: 187 Main Heading: Integer Programming Graphical Solution Key words: integer linear programming solution 48) Consider the following integer linear programming problem Max Z = 3x 1 + 2x 2 Subject to: 3x 1 + 5x 2 ≤ 30 5x 1 + 2x 2 ≤ 28 x 1 ≤ 8 x 1 ,x 2 ≥ 0 and integer The solution to the Linear programming relaxation is: x 1 = 5.714, x 2 = 2.571. What is the optimal solution to the integer linear programming problem? State the optimal values of decision variables and the value of the objective function. Answer: x 1 = 4, x 2 = 3, Z = 18 Diff: 2 Page Ref: 187 Main Heading: Integer Programming Graphical Solution Key words: integer linear programming solution Consider a capital budgeting example with 5 projects from which to select. Let x 1 = 1 if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75, and $300 respectively. The budget is $450. 49) Write the appropriate constraint for the following condition: Choose no fewer than 3 projects. Answer: x 1 +x 2 +x 3 +x 4 +x 5 ≥ 3 Diff: 1 Page Ref: 184 Main Heading: Computer Solution of Integer Program Probs w/Excel, QM for Win Key words: formulation of 0-1 constraints 9 50) Write the appropriate constraint for the following condition: If project 3 is chosen, project 4 must be chosen. Answer: x 3 - x 4 ≤ 0 Diff: 1 Page Ref: 184 Main Heading: Computer Solution of Integer Program Probs w/Excel, QM for Win Key words: formulation of 0-1 constraints 51) Write the appropriate constraint for the following condition: If project 1 is chosen, project 5 must not be chosen. Answer: x 1 + x 5 ≤ 1 Diff: 2 Page Ref: 184 Main Heading: Computer Solution of Integer Program Probs w/Excel, QM for Win Key words: formulation of 0-1 constraints The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. 52) This problem requires 2 different kinds of decision variables. Clearly define each kind. Answer: x a = the number of hoses produced on machine a; y a =1 if machine a is used, 0 if not Diff: 2 Page Ref: 194-195 Main Heading: Integer Programming Models Key words: integer program prob formulation, decision variable definition 53) Write the objective function. Answer: MIN Z = 1.25X 1 + 1.50X 2 + 1.00X 3 + 2.000X 4 + 750Y 1 + 500Y 2 +1000Y 3 + 300Y 4 Diff: 2 Page Ref: 194-195 Main Heading: Integer Programming Models Key words: integer programming problem formulation, model constraints 54) Write a constraint to ensure that if machine 4 is used, machine 1 will not be used. Answer: y 1 + y 4 ≤ 1 Diff: 2 Page Ref: 184 Main Heading: Integer Programming Models Key words: integer programming problem formulation, model constraints 10

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