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# Quantitative Math PERT Project

4. Refer to the LP problem on the next page which represents a model for crashing a PERT
project.

4a). According to the optimal solution, which activities should be crashed and by how many days?
_________________________________

4b). According the model formulation, how much does it cost to crash activity

F?______________

4c). According to the model formulation, which activity is impossible to crash? _______

4d). According to the solution, activity C will be completed by what day of the project?

___________

4e). Management wants the project completed in how many days? ______________

MIN 65YA+50YB+60YC+45YE+70YF
S.T.
1) 1YA<1
2) 1YB<2
3) 1YC<2
4) 1YE<2
5) 1YF<1
6) 1YA+1XA>20
7) 1YB-1XA+1XB>16
8) 1YC-1XB+1XC>18
9) -1XA+1XD>14
10) 1YE-1XD+1XE>19
11) 1YF-1XC+1XF>10
12) 1YF-1XE+1XF>10
13) 1XF<60

Objective Function Value = 280.000

Variable Value Reduced Costs
-------------- --------------- ------------------
YA 1.000 0.000
YB 2.000 0.000
YC 0.000 0.000
YE 1.000 0.000
YF 1.000 0.000
XA 19.000 0.000
XB 33.000 0.000
XC 51.000 0.000
XD 33.000 0.000
XE 51.000 0.000
XF 60.000 0.000

Constraint Slack/Surplus Dual Prices
-------------- --------------- ------------------
1 0.000 40.000
2 0.000 10.000
3 2.000 0.000
4 1.000 0.000
5 0.000 35.000
6 0.000 -105.000
7 0.000 -60.000
8 0.000 -60.000
9 0.000 -45.000
10 0.000 -45.000
11 0.000 -60.000
12 0.000 -45.000
13 0.000 105.000

#### Solution Preview

4. Refer to the LP problem on the next page which represents a model for crashing a PERT
project.

4a). According to the optimal solution, which activities should be crashed and by how many days?
_________________________________
Crash the activity A (YA) by 1 day, activity B (YB)by 2 days, activity E (YE) by 1 day and activity F (YF) by 1 day.
For this see the value of Y variables. The the value is zero, then this activity is not crashed, else the activity is crashed by respective number of days.

4b). According the model formulation, how much does it cost to crash activity

F?______________
It will cost \$70 to crash activity F by 1 day.
The objective function is MIN 65YA+50YB+60YC+45YE+70YF
The cost of crashing activity F is the coefficient of YF in the objectve function.

4c). According to the model formulation, which activity is impossible to crash? _______
Activity D does ...

#### Solution Summary

The solution examines quantitative math for a PERT Project.

\$2.19