Susan Winslow has two alternative routes to travel from her home in Olport to her office in Lewisburg. She can travel on Freeway 5 to Freeway 57 or on Freeway 55 to Freeway 91. The time distributions are as follows:
Freeway 5 | Freeway 57 | Freeway 55 | Freeway 91 | ||||
Relative | Relative | Relative | Relative | ||||
Time | Frequency | Time | Frequency | Time | Frequency | Time | Frequency |
5 | 0.30 | 4 | 0.10 | 6 | 0.20 | 3 | 0.30 |
6 | 0.20 | 5 | 0.20 | 7 | 0.20 | 4 | 0.35 |
7 | 0.40 | 6 | 0.35 | 8 | 0.40 | 5 | 0.20 |
8 | 0.10 | 7 | 0.20 | 9 | 0.20 | 6 | 0.15 |
8 | 0.15 |
Do a five-day simulation of each of the two combinations of routes using the random numbers below. Based on this simulation, which routes should Susan take if her objective is to minimize her total travel time?
Freeway 5 | 63 | 88 | 55 | 46 | 55 |
Freeway 57 | 59 | 09 | 57 | 87 | 07 |
Freeway 55 | 71 | 95 | 83 | 44 | 34 |
Freeway 91 | 51 | 79 | 09 | 67 | 15 |
Then do a 365-day simulation of each of the two combinations of routes using Microsoft Excel. Based on this simulation, are the routes Susan should take different from the above? If so, why?
3. Joe King has ambitions to be mayor of Williston, North Dakota. Joe has determined the breakdown of the steps to the nomination and has estimated normal and crash costs and times for the campaign as follows (times are in weeks).
Normal | Crash | Immediate | |||||
Activity | Time | Cost | Time | Cost | Predecessors | ||
A. | Solicit volunteers | 6 | $5,000 | 4 | $ 9,000 | — | |
B. | Initial "free" exposure | 3 | 4,000 | 3 | 4,000 | — | |
C. | Raise money | 9 | 4,000 | 6 | 10,000 | A | |
D. | Organize schedule | 4 | 1,000 | 2 | 2,000 | A | |
E. | Hire advertising firm | 2 | 1,500 | 1 | 2,000 | B | |
F. | Arrange TV interview | 3 | 4,000 | 1 | 8,000 | B | |
G. | Advertising campaign | 5 | 7,000 | 4 | 12,000 | C, E | |
H. | Personal campaigning | 7 | 8,000 | 5 | 20,000 | D, F |
Joe is not a wealthy man and would like to organize a 16-week campaign at minimum cost. Write and solve a linear program to accomplish this task.
4. The critical path for this network is A - E - F, and the project completion time is 22 weeks.
Activity | Normal | Crash | Normal | Crash |
A | 12 | 8 | 8,000 | 12,000 |
B | 14 | 10 | 5,000 | 7,500 |
C | 8 | 8 | 10,000 | 10,000 |
D | 5 | 3 | 6,000 | 8,000 |
E | 4 | 3 | 5,000 | 7,000 |
F | 6 | 5 | 9,000 | 12,000 |
G | 10 | 8 | 5,000 | 8,000 |
If a deadline of 17 weeks is imposed, give the linear programming model for the crashing decision.
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Advanced-Math: Susan Winslow has two alternative routes to travel from her home in Olport to her office in Lewisburg. She can travel on Freeway 5 to Freeway 57 or on Freeway 55 to Freeway 91. The time distributions are as follows:
Susan Winslow has two alternative routes to travel from her home in Olport to her office in Lewisburg. She can travel on Freeway 5 to Freeway 57 or on Freeway 55 to Freeway 91. The time distributions are as follows:Freeway 5Freeway 57Freeway 55Freeway 91RelativeRelativeRelativeRelativeTimeFrequencyTimeFrequencyTimeFrequencyTimeFrequency50.3040.1060.2030.3060.2050.2070.2040.3570.4060.3580.4050.2080.1070.2090.2060.1580.15Do a five-day simulation of each of the two combinations of routes using the random numbers below. Based on this simulation, which routes should Susan take if her objective is to minimize her total travel time?Freeway 56388554655Freeway...
2. Susan Winslow has two alternative routes to travel from her home in Olport to her office in Lewisburg. She can travel on Freeway 5 to Freeway 57 or on Freeway 55 to Freeway 91. The time distributions are as follows:Freeway 5Freeway 57Freeway 55Freeway 91RelativeRelativeRelativeRelativeTimeFrequencyTimeFrequencyTimeFrequencyTimeFrequency50.3040.1060.2030.3060.2050.2070.2040.3570.4060.3580.4050.2080.1070.2090.2060.1580.15Do a five-day simulation of each of the two combinations of routes using the random numbers below. Based on this simulation, which routes should Susan take if her objective is to minimize her total travel time?Freeway...
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