Question

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 Time	Crash Time	Normal Cost	Crash Cost
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.