Training Major Bill Bligh, Director of the Army War College’s new six-month atta
ID: 3940944 • Letter: T
Question
Training
Major Bill Bligh, Director of the Army War College’s new six-month attaché training program, is concerned about how the 20 officers taking the course spend their time while in his charge. Major Bligh recognizes that there are 168 hours per week and thinks his students have been using them rather inefficiently.
Bligh lets:
X1 = number of hours of sleep needed per week
X2 = number of personal hours
X3 = number of hours of class and studying
X4 = number of hours of social time off base
He thinks that students should study 30 hours a week to have time to absorb the material. This is his most important goal. Bligh feels that students need at most 7 hours of sleep per night on average and that this goal is number 2. He believes that goal number 3 is to provide at least 20 hours per week of social time.
Formulate this goal programming problem
Solve with the software (lindo or excel) of your choice.
Explanation / Answer
Total hours x= 168 hours è 7days
X = 1 week = 168 hours = 7 days + 7 nights
X1 = number of hours of sleep needed per week
Based on goal number 2 students need at most 7 hours of sleep per night on average
So,
X1=7*7 = 49 Hours per week
X3 = number of hours of class and studying
30 hours a week to have time to absorb the material
X3 = 30 hours per week
X4 = number of hours of social time off base
that goal number 3 is to provide at least 20 hours per week of social time.
X4 = 20 hours per week
X2 = number of personal hours
69
X1+X2+ X1+X2 = X
X=168
X1=49
X2=?
X3=30
X4=20
X2 = x-(X1+X2+X3)
X2 = 168-(49+30+20);
X2 = 168-99;
X2 = 99
MAX 2 X4 + S5
ST
X1 + S1 = 168
S1- 0.5 X1 - X2 - S2 = 0
2 X1 + S2 - 0.5 X2 - X3 - S3 = 0
2 X2 + S3 - 0.5 X3 - X4 - S4 = 0
2 X3 + S4 - 0.5 X4 - S5 = 0
END
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