1.
The options from which a decision maker chooses a course of action are
A) called the decision alternatives.
B) under the control of the decision maker.
C) not the same as the states of nature.
D) All of the alternatives are true.
2.
A payoff
A) is always measured in profit.
B) is always measured in cost.
C) exists for each pair of decision alternative and state of nature.
D) exists for each state of nature.
3.
Making a good decision
A) requires probabilities for all states of nature.
B) requires a clear understanding of decision alternatives, states of nature, and payoffs.
C) implies that a desirable outcome will occur.
D) All of the alternatives are true.
4.
A decision tree
A) presents all decision alternatives first and follows them with all states of nature
B) presents all states of nature first and follows them with all decision alternatives.
C) alternates the decision alternatives and states of nature.
D) arranges decision alternatives and states of nature in their natural chronological order.
5.
Which of the methods for decision making without probabilities best protects the decision maker
from undesirable results?
A) the optimistic approach
B) the conservative approach
C) minimum regret
D) minimax regret
6.
When consequences are measured on a scale that reflects a decision maker's attitude toward
profit, loss, and risk, payoffs are replaced by
A) utility.
B) multicriteria measures.
C) sample information
D) opportunity loss.
7.
A decision maker has chosen .4 as the probability for which he cannot choose between a certain
loss of 10,000 and the lottery p(-25000) + (1-p)(5000). If the utility of -25,000 is 0 and of 5000 is
1, then the utility of -10,000 is
A) .5
B) .6
C) .4
D) 4
8.
Lakewood Fashions must decide how many lots of assorted ski wear to order for its three stores.
Information on pricing, sales, and inventory costs has led to the following payoff table, in
thousands.
Demand
Order Size Low
Medium High
1 lot
12
15
15
2 lots
9
25
35
3 lots
6
35
60
a. What decision should be made by the optimist?
b. What decision should be made by the conservative?
c. What decision should be made using minimax regret?
9.
A payoff table is given as
State of Nature
s2
s3
Decision s1
d1
10
8
6
d2
14
15
2
d3
7
8
9
a. What decision should be made by the optimistic decision maker?
b. What decision should be made by the conservative decision maker?
c. What decision should be made under minimax regret?
d. If the probabilities of s1, s2, and s3 are .2, .4, and .4, respectively, then what decision should
be made under expected value?
e. What is the EVPI?
10.
For the payoff table below, the decision maker will use P(s1) = .15, P(s2) = .5, and P(s3) = .35.
State of Nature
s1
s2
s3
Decision
d1
-5,000
1,000
10,000
d2
-15,000
-2,000
40,000
a. What alternative would be chosen according to expected value?
b. For a lottery having a payoff of 40,000 with probability p and -15,000 with probability (1-p),
the decision maker expressed the following indifference probabilities.
Payoff
Probability
10,000
.85
1,000
.60
-2,000
.53
-5,000
.50
c. What alternative would be chosen according to expected utility?
11.
When consequences are measured on a scale that reflects a decision maker's attitude toward
profit, loss, and risk, payoffs are replaced by
A) utility values.
B) multicriteria measures.
C) sample information.
D) opportunity loss.
12.
The purchase of insurance and lottery tickets shows that people make decisions based on
A) expected value.
B) sample information.
C) utility.
D) maximum likelihood.
13.
The expected utility approach
A) does not require probabilities.
B) leads to the same decision as the expected value approach.
C) is most useful when excessively large or small payoffs are possible.
D) requires a decision tree.
14.
Values of utility
A) must be between 0 and 1.
B) must be between 0 and 10.
C) must be nonnegative.
D) must increase as the payoff improves.
15.
A decision maker has chosen .6 as the probability for which she cannot choose between a certain
loss of 10,000 and the lottery of p(5000) + (1 - p)(-25,000). If the utility of -25,000 is 0 and 5000
is 1, then the utility of -10,000 is:
A) .5
B) .6
C) .4
D) 4
16.
When the decision maker prefers a guaranteed payoff value that is smaller than the expected
value of the lottery, the decision maker is:
A) a risk avoider.
B) a risk taker.
C) an optimist.
D) an optimizer.
17.
For a game with an optimal pure strategy, which of the following statements is false?
A) The maximin equals the minimax.
B) The value of the game cannot be improved by either player changing strategies.
C) A saddle point exists.
D) Dominated strategies cannot exist.
18.
A decision maker has the following utility function.
Payoff
Indifference Probability
200
1.00
150
.95
50
.75
0
.60
-50
0
What is the risk premium for the payoff of 50?
19.
Super Cola is considering the introduction of a new 8 oz. root beer. The probability that the root
beer will be a success is believed to equal 0.6. The payoff table is as follows:
Success (s1)Failure (s2)
Produce
$250,000 -$300,000
Do Not Produce-$50,000 -$20,000
Company management has determined the following utility values:
Amount $250,000 -$20,000 -$50,000 -$300,000
Utility
100
60
55
0
a. Is the company a risk taker, risk averse, or risk neutral?
b. What is Super Cola's optimal decision?
20.
Consider the following two-person zero-sum game. Assume the two players have the same two
strategy options. The payoff table shows the gains for Player A.
Player B
Player A
Strategy b1 Strategy b2
Strategy α1 3
9
Strategy α2 6
2
Determine the optimal strategy for each player. What is the value of the game?
21.
The maximization or minimization of a quantity is the:
A)
B)
C)
D)
goal of management science.
B) decision for decision analysis.
C) constraint of operations research.
D) objective of linear programming.
22.
Decision variables
A) tell how much or how many of something to produce, invest, purchase, hire, etc.
B) represent the values of the constraints.
C) measure the objective function.
D) must exist for each constraint.
23.
Which of the following is a valid objective function for a linear programming problem?
A) Max 5xy
B) B) Min 4x + 3y + (2/3)z
C) Max 5x2 + 6y2
D) Min (x1 + x2)/x3
24.
Which of the following statements is NOT true?
A) A feasible solution satisfies all constraints.
B) An optimal solution satisfies all constraints.
C) An infeasible solution violates all constraints.
D) A feasible solution point does not have to lie on the boundary of the feasible region.
25.
Slack
A)
B)
C)
D)
is the difference between the left and right sides of a constraint.
is the amount by which the left side of a constraint is smaller than the right side.
is the amount by which the left side of a constraint is larger than the right side.
exists for each variable in a linear programming problem.
26.
To find the optimal solution to a linear programming problem using the graphical method
A) find the feasible point that is the farthest away from the origin
B) find the feasible point that is at the highest location.
C) find the feasible point that is closest to the origin.
D) None of the alternatives is correct.
27.
Infeasibility means that the number of solutions to the linear programming models that satisfies
all constraints is:
A) at least 1.
B) 0.
C) an infinite number.
D) at least 2.
28.
All linear programming problems have all of the following properties EXCEPT
A) a linear objective function that is to be maximized or minimized.
B) a set of linear constraints
C) alternative optimal solutions.
D) variables that are all restricted to nonnegative values.
29.
Solve the following system of simultaneous equations. 6X + 2Y = 50. 2X + 4Y = 20.
30.
Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot
of pens are given below.
Fliptop Model
Tiptop Model Available
Plastic
3
4
36
Ink Assembly 5
4
40
Molding Time 5
2
30
The profit for either model is $1000 per lot.
a. What is the linear programming model for this problem?
b. Find the optimal solution.
c. Will there be excess capacity in any resource? If so, how much excess capacity?
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