1) solve the following equation by using Big-M method.
Minimize z = 4x_{1} + 3x_{2}
Subjected to 2x_{1} + x_{2} ≥ 10
-3x_{1} + 2x_{2} ≤ 6
x_{1} + x_{2} ≥ 6 and x_{1}, x_{2} ≥ 0
2) Minimize the time required to process the jobs on the machines given below, that is, for each machine state the job that must be done first by using graphical method. Also compute the total elapsed time to complete both jobs.
Sequence: A B C D E
Job 1 Time (hr): 6 8 4 12 4
Sequence: B C A D E
Job 2 Time (hr): 10 8 6 4 12
3) Small project is composed of activities whose time estimates are given in the table below.
Activity : 1-2 1-3 1-4 2-5 3-5 4-6 5-6
Optimistic time
Estimate : 1 1 2 1 2 2 3
Most likely time : 1 4 2 1 5 5 6
Pessimistic Time : 7 7 8 1 14 8 15
a) Sketch the project network and identity all the paths through it.
b) Determine the expected duration and variance of each activity.
c) Determine the expected project length?
d) Compute the variance and standard deviation of project length
e) If project due date is 18 weeks, find the probability of not meeting due date?
f) What due date has about 90% chance of being met?