Part A-
1. A project network is shown below. Use a forward and a backward pass to determine the critical path, and then fill out the table below.
| Activity |
Precedence Activities |
Activity Time (weeks) |
ES |
LS |
EF |
LF |
Slack |
Critical Path? |
| A |
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| B |
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| C |
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| D |
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| E |
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| F |
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| G |
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| H |
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| I |
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Now assume that the times listed are only the expected times instead of being fixed times. Is the probability of being finished in fewer than 25 weeks more or less than 50%?
2. Given this network with activities and times estimated in days,
| Activity |
Optimistic |
Most Probable |
Pessimistic |
| A |
2 |
5 |
6 |
| B |
1 |
3 |
7 |
| C |
6 |
7 |
10 |
| D |
5 |
12 |
14 |
| E |
3 |
4 |
5 |
| F |
8 |
9 |
12 |
| G |
4 |
6 |
8 |
| H |
3 |
6 |
8 |
| I |
5 |
7 |
12 |
| J |
12 |
13 |
14 |
| K |
1 |
3 |
4 |
a. What are the critical path activities?
b. What is the expected time to complete the project?
c. What is the probability the project will take more than 28 days to complete?
Part B-
1. Greenfields is a mail order seed and plant business. The size of orders is uniformly distributed over the interval from $25 to $80. Use the following random numbers to generate the size of 10 orders.
41 .99 .07 .05 .38 .77 .19 .12 .58 .60
2. An airline reservation system first asks customers whether they want to schedule a domestic or an international flight. Sixty-five percent of the reservations are for domestic flights. The time distribution of advance sales is also important, and it is given below.
a. Place the appropriate random number ranges in the tables above.
b. Set up and perform a simulation for three customers. Determine whether they want a domestic or international flight, and how far in advance the reservation is being made. Use random numbers from this list:
.632 .715 .998 .671 .744 .021