Chapter 7 Linear Programming Models Graphical and Computer Methods Part 2

45) Which of the following is not acceptable as a constraint in a linear programming problem (maximization)? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) None of the above Answer: A Diff: 2 Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 46) If one changes the contribution rates in the objective function of an LP, A) the feasible region will change. B) the slope of the isoprofit or isocost line will change. C) the optimal solution to the LP is sure to no longer be optimal. D) All of the above E) None of the above Answer: B Diff: 2 Topic: SENSITIVITY ANALYSIS 47) Sensitivity analysis may also be called A) postoptimality analysis. B) parametric programming. C) optimality analysis. D) All of the above E) None of the above Answer: D Diff: 2 Topic: SENSITIVITY ANALYSIS 48) Sensitivity analyses are used to examine the effects of changes in A) contribution rates for each variable. B) technological coefficients. C) available resources. D) All of the above E) None of the above Answer: D Diff: 2 Topic: SENSITIVITY ANALYSIS 11 49) Which of the following is a basic assumption of linear programming? A) The condition of uncertainty exists. B) Independence exists for the activities. C) Proportionality exists in the objective function and constraints. D) Divisibility does not exist, allowing only integer solutions. E) Solutions or variables may take values from -∞ to +∞. Answer: C Diff: 2 Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 50) The condition when there is no solution that satisfies all the constraints simultaneously is called A) boundedness. B) redundancy. C) optimality. D) dependency. E) None of the above Answer: E Diff: 2 Topic: FOUR SPECIAL CASES IN LP 51) If the addition of a constraint to a linear programming problem does not change the solution, the constraint is said to be A) unbounded. B) non-negative. C) infeasible. D) redundant. E) bounded. Answer: D Diff: 2 Topic: FOUR SPECIAL CASES IN LP 52) Which of the following is not an assumption of LP? A) simultaneity B) certainty C) proportionality D) divisibility E) additivity Answer: A Diff: 2 Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 12 53) The difference between the left-hand side and right-hand side of a less-than-or-equal-to constraint is referred to as A) surplus. B) constraint. C) slack. D) shadow price. E) None of the above Answer: C Diff: 2 Topic: LINEAR PROGRAMMING MODELS: GRAPHICAL AND COMPUTER METHODS 54) The difference between the left-hand side and right-hand side of a greater-than-or-equal-to constraint is referred to as A) surplus. B) constraint. C) slack. D) shadow price. E) None of the above Answer: A Diff: 2 Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 55) A constraint with zero slack or surplus is called a A) nonbinding constraint. B) resource constraint. C) binding constraint. D) nonlinear constraint. E) linear constraint. Answer: C Diff: 1 Topic: SOLVING FLAIR FURNITURE’S LP PROBLEM USING QM FOR WINDOWS AND EXCEL 56) A constraint with positive slack or surplus is called a A) nonbinding constraint. B) resource constraint. C) binding constraint. D) nonlinear constraint. E) linear constraint. Answer: A Diff: 1 Topic: SOLVING FLAIR FURNITURE’S LP PROBLEM USING QM FOR WINDOWS AND EXCEL 13 57) The increase in the objective function value that results from a one-unit increase in the right-hand side of that constraint is called A) surplus. B) shadow price. C) slack. D) dual price. E) None of the above Answer: B Diff: 2 Topic: SENSITIVITY ANALYSIS 58) A straight line representing all non-negative combinations of X1 and X2 for a particular profit level is called a(n) A) constraint line. B) objective line. C) sensitivity line. D) profit line. E) isoprofit line. Answer: E Diff: 2 Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 59) In order for a linear programming problem to have a unique solution, the solution must exist A) at the intersection of the non-negativity constraints. B) at the intersection of a non-negativity constraint and a resource constraint. C) at the intersection of the objective function and a constraint. D) at the intersection of two or more constraints. E) None of the above Answer: D Diff: 2 Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM 60) In order for a linear programming problem to have multiple solutions, the solution must exist A) at the intersection of the non-negativity constraints. B) on a non-redundant constraint parallel to the objective function. C) at the intersection of the objective function and a constraint. D) at the intersection of three or more constraints. E) None of the above Answer: B Diff: 2 Topic: FOUR SPECIAL CASES IN LP 14 61) Consider the following linear programming problem: The maximum possible value for the objective function is A) 360. B) 480. C) 1520. D) 1560. E) None of the above Answer: E Diff: 3 Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM AACSB: Analytic Skills 62) Consider the following linear programming problem: Which of the following points (X,Y) is feasible? A) (10,120) B) (120,10) C) (30,100) D) (60,90) E) None of the above Answer: C Diff: 2 Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM AACSB: Analytic Skills 15 63) Consider the following linear programming problem: Which of the following points (X,Y) is in the feasible region? A) (30,60) B) (105,5) C) (0,210) D) (100,10) E) None of the above Answer: D Diff: 2 Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM AACSB: Analytic Skills 64) Consider the following linear programming problem: Which of the following points (X,Y) is feasible? A) (50,40) B) (30,50) C) (60,30) D) (90,20) E) None of the above Answer: C Diff: 2 Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM AACSB: Analytic Skills 65) Which of the following is not an assumption of LP? A) certainty B) proportionality C) divisibility D) multiplicativity E) additivity Answer: D Diff: 2 Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 16 66) Consider the following linear programming problem: This is a special case of a linear programming problem in which A) there is no feasible solution. B) there is a redundant constraint. C) there are multiple optimal solutions. D) this cannot be solved graphically. E) None of the above Answer: B Diff: 3 Topic: FOUR SPECIAL CASES IN LP AACSB: Analytic Skills 67) Which of the following functions is not linear? A) 5X + 3Z B) 3X + 4Y + Z - 3 C) 2X + 5YZ D) Z E) 2X - 5Y + 2Z Answer: C Diff: 1 Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 68) Which of the following is not one of the steps in formulating a linear program? A) Graph the constraints to determine the feasible region. B) Define the decision variables. C) Use the decision variables to write mathematical expressions for the objective function and the constraints. D) Identify the objective and the constraints. E) Completely understand the managerial problem being faced. Answer: A Diff: 2 Topic: FORMULATING LP PROBLEMS 17 69) Which of the following is not acceptable as a constraint in a linear programming problem (minimization)? A) Constraint 1 B) Constraint 2 C) Constraint 3 D) Constraint 4 E) Constraint 5 Answer: E Diff: 2 Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM 70) What type of problems use LP to decide how much of each product to make, given a series of resource restrictions? A) resource mix B) resource restriction C) product restriction D) resource allocation E) product mix Answer: E Diff: 2 Topic: FORMULATING LP PROBLEMS 71) Consider the following linear programming problem: This is a special case of a linear programming problem in which A) there is no feasible solution. B) there is a redundant constraint. C) there are multiple optimal solutions. D) this cannot be solved graphically. E) None of the above Answer: B Diff: 3 Topic: FOUR SPECIAL CASES IN LP AACSB: Analytic Skills 18 72) Consider the following constraints from a linear programming problem: 2X + Y ≤ 200 X + 2Y ≤ 200 X, Y ≥ 0 If these are the only constraints, which of the following points (X,Y) cannot be the optimal solution? A) (0, 0) B) (0, 200) C) (0,100) D) (100, 0) E) (66.67, 66.67) Answer: B Diff: 3 Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM AACSB: Analytic Skills 73) Consider the following constraints from a linear programming problem: 2X + Y ≤ 200 X + 2Y ≤ 200 X, Y ≥ 0 If these are the only constraints, which of the following points (X,Y) cannot be the optimal solution? A) (0, 0) B) (0, 100) C) (65, 65) D) (100, 0) E) (66.67, 66.67) Answer: C Diff: 3 Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM AACSB: Analytic Skills 74) A furniture company is producing two types of furniture. Product A requires 8 board feet of wood and 2 lbs of wicker. Product B requires 6 board feet of wood and 6 lbs of wicker. There are 2000 board feet of wood available for product and 1000 lbs of wicker. Product A earns a profit margin of $30 a unit and Product B earns a profit margin of $40 a unit. Formulate the problem as a linear program. Answer: Diff: 2 Topic: FORMULATING LP PROBLEMS 19 AACSB: Analytic Skills 75) As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model is $12 per unit and the Special's profit is $10. Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The company has also decided that the Special model must comprise at least 40 percent of the production total. (a) Formulate this as a linear programming problem. (b) Find the solution that gives the maximum profit. Answer: (b) Optimal solution: X1 = 120, X2 = 240 Profit = $3,840 Diff: 3 Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP PROBLEM AACSB: Analytic Skills 20