Chapter 3
The region that satisfies all of the constraints in linear programming is called the region of optimality.
False
Linear programming is an appropriate problem-solving technique for decisions that have no alternative courses of action.
False
The maximax criterion of decision making requires that all decision alternatives have an equal probability of occurrence.
False
In a decision tree, a square symbol represents a state of nature node.
False
Expected monetary value is most appropriate for problem solving that takes place: A. under conditions of risk. .B. under conditions of uncertainty. C. when conditions are average. D. when all alternatives are equally likely. E. when all states of nature are equally likely.
A
If cars sell for $500 profit and trucks sell for $300 profit, which of the following represents the objective function? A. Maximize profit = 500C + 300T B. Maximize profit = 800(T + C) C. Maximize profit = 500C minus− 300T D. Minimize profit = 500C + 300T E. Minimize profit = 300T minus− 500C
A
In linear programming, a statement such as "maximize contribution" becomes an objective function when the problem is formulated.
True
In linear programming, statements such as "the blend must consist of at least 10% of ingredient A, at least 30% of ingredient B, and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100 percent.
True
In sensitivity analysis, a zero shadow price (or dual value) for a resource ordinarily means that the resource has not been used up.
True
Linear programming helps operations managers make decisions necessary to make effective use of resources such as machinery, labor, money, time, and raw materials.
True
A decision maker using the maximin criterion on the problem above would choose Alternative ________ because the maximum of the row minimums is ________. A. C; 70 B. D; 140 C. B; 30 D. D; 10 E. A; 55
A
In terms of decision theory, an occurrence or situation over which the decision maker has no control is called a(n): A. state of nature. B. decision tree. C. alternative. D. EMV. E. decision under uncertainty.
A
What is a tabular presentation that shows the outcome for each decision alternative under the various possible states of nature called? A. payoff table .B. decision tree C. feasible region D. payback period matrix E. isoquant table
A
When solving decision trees, what phrase represents the act of dropping an alternative from consideration because it is less favorable than another available option? A. prune the branch B. punt the ball C. open the hatch D. shake the tree E. cut the leaf
A
A decision maker using the maximax criterion on the problem above would choose Alternative ________ because the maximum of the row maximums is ________. A. D; minus−100 B. D; 140 C. A; 60 D. B; 80 E. C; 70
B
The expected value with perfect information: A. is the average of the maximax and the maximin. B. is an input into the calculation of the expected value of perfect information. .C. equals EVPI − Maximum EMV. D. requires that each decision alternative have a known probability of occurrence. E. None of the above
B
The feasible region in the diagram below is consistent with which one of the following constraints? A. 8X1 minus− 4X2 less than or equals≤ 160 B. 8X1 + 4X2 greater than or equals≥ 160 C. 4X1 minus− 8X2 less than or equals≤ 160 D. 8X1 + 4X2 less than or equals≤ 160 E. 4X1 + 8X2 less than or equals≤ 160
B
The last step of the decision-making process is to: A. select the best alternative. B. implement the decision. C. develop a model. D. evaluate each alternative. E. check the decision with senior management.
B
There are three equally likely states of nature (High, Medium, and Low demand). If the large factory will post profits of $50,000, $25,000, and minus− $10,000 under these states of nature, respectively, what is the EMV of the factory? A. $25,000 B. $21,666.67 C. $50,000 D. $28,333.33 E. $65,000
B
What is the difference between the expected payoff under perfect information and the maximum expected payoff under risk? A. expected monetary value B. expected value of perfect information C. expected monetary payoff D. economic order quantity E. PERT
B
A decision maker who uses the maximin criterion when solving a problem under conditions of uncertainty is: A. an optimist. B. an economist. C. a pessimist. D. an optometrist. E. making a serious mistake; maximin is not appropriate for conditions of uncertainty.
C
A plant manager wants to know how much he should be willing to pay for perfect market research. Currently there are two states of nature facing his decision to expand or do nothing. Under favorable market conditions the manager would make $100,000 for the large plant and $5,000 for the small plant. Under unfavorable market conditions the large plant would lose $50,000 and the small plant would make $0. If the two states of nature are equally likely, how much should he pay for perfect information? A. $145,000 B. $100,000 C. $25,000 D. $0 E. $50,000
C
What decision criterion would be used by an optimistic decision maker solving a problem under conditions of uncertainty? A. minimin B. expected monetary value C. maximax D. maximin E. equally likely
C
A square node on a decision tree infers that: A. the node splits into various states of nature, of which only one will occur. B. there are several alternatives available. .C. the manager must choose an alternative. D. Both B and C. E. A, B, and C.
D
The feasible region in the diagram below is consistent with which one of the following constraints? A. 8X1 minus− 4X2 less than or equals≤ 160 B. 4X1 + 8X2 less than or equals≤ 160 C. 4X1 minus− 8X2 less than or equals≤ 160 D. 8X1 + 4X2 less than or equals≤ 160 .E. 8X1 + 4X2 greater than or equals≥ 160
D
Which of the following represents a valid constraint in linear programming? A. 2X greater than or equals≥ 7XY B. (2X)(7Y) greater than or equals≥ 500 C. 2X2 + 7Y greater than or equals≥ 50 D. 2X + 7Y greater than or equals≥100 Your answer is correct.E. All of the above are valid linear programming constraints.
D
Doing nothing would yield how much profit if favorable market conditions prevail according to the following profit decision table? A. $5,000 B. $0 C. $10,000 D. −$10,000 E. $20,000
E
In which of the following has LP been applied successfully? A. determining the distribution system for multiple warehouses to multiple destinations B. minimizing 911 response time for police patrols C. minimizing distance traveled by school buses carrying children D. minimizing labor costs for bank tellers while maintaining service levels E. all of the above
E
The first step, and a key element, in the decision-making process is to: A. develop objectives. B. select the best alternative. C. monitor the results. D. consult a specialist. E. clearly define the problem.
E
What is the outcome of an alternative/state of nature combination called? A. price B. conditional expectation C. conditional probability D. expected value E. conditional value
E
Which of the following is NOT considered a step in the decision-making process? A. Evaluate each alternative solution based on its merits and drawbacks. B. Develop specific and measurable objectives. C. Clearly define the problem and the factors that influence it. D. Select the best alternative. E. Minimize costs whenever possible.
E
An example of expected monetary value would be the payoff from selecting a particular alternative when a particular state of nature occurs.
False
Constraints are needed to solve linear programming problems by hand, but not by computer.
False
Decision trees and decision tables can both solve problems requiring a single decision, but decision tables are the preferred method when a sequence of decisions is involved.
False
For a linear programming problem with the constraints 2X + 4Y less than or equals≤ 100 and 1X + 8Y less than or equals≤ 100, two of its corner points are (0, 0) and (0, 25).
False
If a decision maker can assign probabilities of occurrences to the states of nature, then the decision-making environment is Decision Making under Uncertainty.
False
If a decision maker has to make a particular decision only once, expected monetary value is a good indication of the payoff associated with the decision.
False
In linear programming, if there are three constraints, each representing a resource that can be used up, the optimal solution must use up all of each of the three resources.
False
In terms of linear programming, the fact that the solution is infeasible implies that the "profit" can increase without limit.
False
In the graphical solution to a linear program, the region that satisfies the constraint 4X + 15Z greater than or equals≥ 1000 includes the origin of the graph.
False
Solving a linear programming problem with the iso-profit line solution method requires that we move the iso-profit line to each corner of the feasible region until the optimum is identified.
False
The expected value of perfect information is the same as the expected value with perfect information.
False
The expected value with perfect information assumes that all states of nature are equally likely.
False
The last step in the analytic decision process is to clearly define the problem and the factors that influence it.
False
A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.
True
An example of a conditional value would be the payoff from selecting a particular alternative when a particular state of nature occurs.
True
If a decision maker knows for sure which state of nature will occur, he/she is making a decision under certainty.
True
In a decision tree, the expected monetary values are computed by working from right to left.
True
Sensitivity analysis can be applied to linear programming solutions by either (1) trial and error or (2) the analytic postoptimality method.
True
The expected monetary value of a decision alternative is the sum of all possible payoffs from the alternative, each weighted by the probability of that payoff occurring.
True
The maximin criterion is pessimistic, while the maximax criterion is optimistic.
True
The optimal solution to a linear programming problem lies within the feasible region.
True