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