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front 1 Suppose that a firm makes gears (G) and axles (A). Each gear requires 15 minutes of labor and each axle requires 30 minutes of labor. One thousand hours of labor are available. How should the labor constraint(s) be written? | back 1 .25G + .5A ≤ 1000 |

front 2 If a firm is using a linear program to determine production amounts of its chairs and tables, which of the following constraints must be in the model? | back 2 non-negativity |

front 3 What does LP stand for? | back 3 Linear Program |

front 4 Sausage and Cheese Ltd. prepares three gift packages containing sausages and cheeses. The "Tasters," "Succulent," and "Gourmet" gift packages contain 3 sausages and 6 cheeses, 5 sausages and 4 cheeses, and 6 sausages and 5 cheeses, respectively. There are 2500 sausages and 3000 cheeses available for packing, and demand is unlimited. Profits are $2.50, $3.50, and $4.00 for the "Tasters," "Succulent," and "Gourmet" gift packages, respectively. The goal is to maximize profits. Let T, S, and G represent the number of gift packages produced of type "Tasters," "Succulent," and "Gourmet," respectively. What is the objective function for this linear program? | back 4 Max 2.5T + 3.5S + 4G |

front 5 Which of the following statements is not correct? | back 5 A Linear Program as described in Supplement B can have more than one objective function if it has only one constraint. |

front 6 What is the optimal solution (X, Y, Z) to the following linear
program? | back 6 (0, 20, 0) |

front 7 Consider the following constraints from a two-variable Linear
Program. | back 7 (50, 0) |

front 8 Consider the following three functions: | back 8 h and i are linear, but g is not linear |

front 9 George Dantzig developed the ___________________ in 1947 to solve Linear Programs. | back 9 Simplex Method |

front 10 When was the Simplex Method developed? | back 10 1947 |

front 11 A constraint in Excel Solver consists of what three pieces of information? | back 11 Cell Reference, relationship operator, and Constraint |

front 12 In the "Solver Options" box of Excel Solver, what should be checked to ensure that all decision variables are ≥ 0? | back 12 Assume Non-Negative |

front 13 In the "Solver Options" box of Excel Solver, what should be checked to ensure that the Simplex Method is used to solve the model? | back 13 Assume Linear Model |

front 14 In the "Solver Parameters" box of Excel Solver, what is clicked to actually solve the problem? | back 14 "SOLVE" |

front 15 Three reports are available when Solver has successfully found an optimal solution. These are _______. | back 15 Answer Report, Sensitivity Report, and Limits Report |

front 16 The ________________________ for a constraint is the amount the optimal objective value will change if the right-hand-side of the constraint is increased by one unit. | back 16 Shadow Price |

front 17 One use of the Answer report is: | back 17 as a debugging tool. |

front 18 In Linear Programming models, what do you want to do with the objective? | back 18 maximize or minimize |

front 19 A mathematical model in which one is trying to maximize or minimize some quantity while satisfying a set of constraints is a(n): | back 19 constrained optimization problem |

front 20 Human intelligence is not needed in which of the following steps of solving optimization problems? | back 20 solving the problem |

front 21 Once you've written the algebraic formulation of the problem, the next setup involved in Solving Optimization Problems is: | back 21 set up the Solver settings |

front 22 A ____________________ contains explicit definitions of the decision variables, an algebraic expression of the objective function, and algebraic statements of the constraints. | back 22 formulation |

front 23 When formulating optimization problems, which of the following represent the typical sequence? | back 23 (1) diagram, (2) text-based formulation, (3) algebraic formulation |

front 24 A diagram of the situation can help _______ the problem as well as be a(n) ______ _______ tool. | back 24 structure, valuable communication |

front 25 The algebraic formulation of an optimization problem must state what three things? | back 25 decision variables, objective function, and constraints |

front 26 What are the allowable constraint relationship types in optimization problems? | back 26 =, ≤, ≥ |

front 27 If C represents the number of chairs produced, which of the following is a proper non-negativity constraint? | back 27 C ≥ 0 |

front 28 Which type of constraint does not allow the solution for a decision variable of an optimization problem to be less than zero? | back 28 non-negativity |

front 29 Testing of the LP model should include __________ and _____________. | back 29 base case, test values |

front 30 How can the following Linear Program be characterized? | back 30 bounded and infeasible |

front 31 Consider the following three functions: | back 31 g(x, y) is linear, but f(x) and h(x, y) are not linear |

front 32 Sausage and Cheese Ltd. prepares three gift packages containing sausages and cheeses. The "Tasters," "Succulent," and "Gourmet" gift packages contain 3 sausages and 6 cheeses, 5 sausages and 4 cheeses, and 6 sausages and 5 cheeses, respectively. There are 2500 sausages and 3000 cheeses available for packing, and demand is unlimited. Profits are $2.50, $3.50, and $4.00 for the "Tasters," "Succulent," and "Gourmet" gift packages, respectively. The goal is to maximize profits. Let T, S, and G represent the number of gift packages produced of type "Tasters," "Succulent," and "Gourmet," respectively. What is the constraint describing the sausage capacity? | back 32 3T + 5S + 6G ≤ 2500 |

front 33 Dane's aircraft muffler manufacturers have 1500 linear feet of steel on hand to manufacture the three top selling muffler sets. Super mufflers (S) provide $285 profit and common (C) mufflers' profit margin is $310, while the deluxe (D) muffler set provides a $400 profit margin. It costs Dane $310, $295, and $400 to build each muffler set, respectively. What is the objective function of Dane's aircraft muffler manufacturing? | back 33 Max 285S + 310C + 400D |

front 34 How can the following Linear Program be characterized? | back 34 bounded and feasible |

front 35 Capital Co. is considering five different projects. Define Xi as a binary (0-1) variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1,2,3,4,5. Which of the following represents the constraint(s) stating that projects 2, 3, and 4 cannot all be undertaken simultaneously? | back 35 X2 + X3 + X4 ≤ 2 |

front 36 Which of the following is not one of the steps in setting up the Solver optimization problem? | back 36 specify the constraints |

front 37 Solver provides many options for the solution process. For LPs, the two most commonly used are: | back 37 assume linear model, assume non-negative |

front 38 Consider a mathematical program where Xi represents the amount produced of item i (i = 1,2,3,4), and you want the total amount produced over all four items to equal either 100, 120, 140, or 200. If you define qi as binary (0-1) variables (i = 1,2,3,4) and add the constraint q1 + q2 + q3 + q4 = 1, what other constraint do you need to add to the program? | back 38 X1 + X2 + X3 + X4 = 100q1 + 120q2 + 140q3 + 200q4 |

front 39 Consider the mathematical program below. Which of the following
choices represents an upper bound to the problem? | back 39 X = 0 |

front 40 Consider the Linear Program below. Which of the choices represents
the best (tightest) lower bound? | back 40 (5, 0) |

front 41 How can the following Linear Program be characterized? | back 41 bounded and feasible |

front 42 How can the following Linear Program be characterized? | back 42 unbounded and feasible |

front 43 Consider the following constraints from a two-variable Linear
Program. | back 43 (10, 10) |

front 44 Consider the following constraints from a two-variable Linear
Program. | back 44 (9, 5) |

front 45 For an optimization problem a(an) __________________ violates at least one of the constraints. | back 45 infeasible solution |

front 46 If the solution to an optimization problem violates two constraints but satisfies three, it is a(an) ________. | back 46 infeasible solution |

front 47 The two primary Excel tools for diagnosing problems in models are ___________________. | back 47 Error Checking and Formula Auditing |

front 48 Which Excel tool provides solutions to Linear Programs? | back 48 Solver |

front 49 What in Excel Solver corresponds to the objective function in the algebraic model? | back 49 Target Cell |

front 50 What in Excel Solver corresponds to the decision variables in the algebraic model? | back 50 Changing Cells |

front 51 In the Excel Solver "Add Constraint" box, what two additional choices are available under the relationship operator list besides ≤, ≥, and =? | back 51 int and bin |

front 52 Constraints at their limits at the optimal solution of a Linear Program, that is, with the left-hand-side value equal to the right-hand-side value, are called _________________________. | back 52 binding constraints |

front 53 Constraints that are not at their limits at the optimal solution of a Linear Program, that is, with the left-hand-side value not equal to the right-hand-side value, are called _________________________. | back 53 non-binding constraints |

front 54 To retain model flexibility while using Solver you must: | back 54 use only cell references |

front 55 At the optimal solution of a Linear Program, the difference between the right-hand-side value and the left-hand-side value of a constraint is the ____________________. | back 55 slack |

front 56 The Answer Report Target Cell, Adjustable Cell, and Constraint sections all include: | back 56 original value, final value |

front 57 What do you need to do before using Solver? | back 57 have a working, flexible spreadsheet model |

front 58 Consider the following three functions: | back 58 g and i are linear, but h is not linear |

front 59 Consider the following two functions: | back 59 g(x, y) is linear, but h(x, y) is not linear |

front 60 How can the following Linear Program be characterized? | back 60 unbounded and feasible |

front 61 In Linear Programming models, over what quantities do you have control? | back 61 decision variables |

front 62 What is the optimal solution to the following linear
program? | back 62 the program is infeasible |

front 63 Which of the following statements is correct? | back 63 Given a Linear Program with a maximization objective, the optimal objective function value may decrease if a ≥ constraint is added to the program. |

front 64 The text-based formulation of an optimization problem should state what three things? | back 64 decision variables, objective function, and constraints |