Maths Multiple Choice Questions

Question 1
Arcs in a project network indicate

completion times.
precedence relationships.
activities.
the critical path.

Question 2
The critical path
is any path that goes from the starting node to the completion node.
is a combination of all paths.
is the shortest path.
is the longest path.

Question 3
Activities following a node

can begin as soon as any activity preceding the node has been completed.
have an earliest start time equal to the largest of the earliest finish times for all activities entering the node.
have a latest start time equal to the largest of the earliest finish times for all activities entering the node.
None of the alternatives is correct.

Question 4
Slack equals

LF – EF.
EF + LF.
EF – LS.
LF – ES.

Question 5
Activities with zero slack

can be delayed.
must be completed first.
lie on a critical path.
have no predecessors.

Question 6
Which of the following is always true about a critical activity:

LS = EF.
LF = LS.
ES = LS.
EF = ES.

Question 7

The following schedule of activities applies to a certain project.

Activity
Precedence
Activities
Time (weeks)

A
--
5
B
--
4
C
--
8
D
A, B
4
E
C
12
F
C
10
G
A, D, E
3
H
E
0
I
E, F
5

Finish

G, H, I

Use a forward and a backward pass to determine the critical path and project length, and then fill out the table below (copy and paste the table to the answer box).

Activity Precedence
Activities Activity Time
(weeks) ES LS EF LF Slack
A - 5 0 13 5 18 13
B - 4 0 14 4 18 14
C - 8 0 0 8 8 0
D A,B 4 5 18 9 22 13
E C 12 8 8 20 20 0
F C 10 8 10 18 20 2
G A, D, E 3 20 22 23 25 2
H E 0 20 25 20 25 5
I E, F 5 20 20 25 25 0
Finish G,H, I -- -- --   -- --

Question 8
state is part of a system.
system is in a particular state at a given time.
time has reached a steady state.
transition will occur.

Question 9

For a situation with weekly dining at either an Italian or Mexican restaurant,
the weekly visit is the trial and the restaurant is the state.
the weekly visit is the state and the restaurant is the trial.
the weekly visit is the trend and the restaurant is the transition.
the weekly visit is the transition and the restaurant is the trend.

Question 10
A transition probability describes

the probability of a success in repeated, independent trials.
the probability a system in a particular state now will be in a specific state next period.
the probability of reaching an absorbing state.
None of the alternatives is correct.

Question 11
The probability of going from state 1 in period 2 to state 4 in period 3 is

p12
p23
p14
p43

Question 12

The probability a system is in a particular state after a large number of periods is
independent of the beginning state of the system.
dependent on the beginning state of the system.
equal to one half.
the same for every ending system

Question 13

The daily price of a farm commodity is up, down, or unchanged from the day before. Analysts predict that if the last price was down, there is a .5 probability the next will be down, and a .4 probability the price will be unchanged. If the last price was unchanged, there is a .35 probability it will be down and a .35 probability it will be up. For prices whose last movement was up, the probabilities of down, unchanged, and up are .1, .3, and .6.
a. Construct the matrix of transition probabilities.
b. Provide (but do not solve) a system of equations for calculating the steady state probabilities.