Chapter 11.5, Problem 7E

(a)

To determine

The type of scheduling problem. Also, draw the appropriate directed network.

Suppose we want to build a Klein bottle. The tasks involved in this project and the time required for each are recorded in the following table.

Code	Tasks	Time (in months)
G	blow glass	7
Po	Polish	5
Sh	Shape	9
A	Add hole	4
H	Affix handles	5
Tw	Twist	2
R	Remove hole	4
Pa	paint	6

The glass must be blown before anything else. Polishing precedes all but G and Sh; shping precedes all but G and Po. The hole must be added before it removed (!) and before the bottle is twisted. The handles go on before Tw and Pa. Once Tw, R, and Pa are completed, the project is finished.

(b)

To determine

All critical paths for this project. Suppose we want to build a Klein bottle. The tasks involved in this project and the time required for each are recorded in the following table.

Code	Tasks	Time (in months)
G	blow glass	7
Po	Polish	5
Sh	Shape	9
A	Add hole	4
H	Affix handles	5
Tw	Twist	2
R	Remove hole	4
Pa	paint	6

The glass must be blown before anything else. Polishing precedes all but G and Sh; shping precedes all but G and Po. The hole must be added before it removed (!) and before the bottle is twisted. The handles go on before Tw and Pa. Once Tw, R, and Pa are completed, the project is finished.

(c)

To determine

The slack of Po, Sh, A, Tw and R for each of the critical paths found in (b).Suppose we want to build a Klein bottle. The tasks involved in this project and the time required for each are recorded in the following table.

Code	Tasks	Time (in months)
G	blow glass	7
Po	Polish	5
Sh	Shape	9
A	Add hole	4
H	Affix handles	5
Tw	Twist	2
R	Remove hole	4
Pa	paint	6

The glass must be blown before anything else. Polishing precedes all but G and Sh; shping precedes all but G and Po. The hole must be added before it removed (!) and before the bottle istwisted. The handles go on before Tw and Pa. Once Tw, R, and Pa are completed, the project is finished.

(d)

To determine

The completion of the project be delayed. Suppose that tasks Po and A are each delayed 3 months. Suppose we want to build a Klein bottle. The tasks involved in this project and the time required for each are recorded in the following table.

Code	Tasks	Time (in months)
G	blow glass	7
Po	Polish	5
Sh	Shape	9
A	Add hole	4
H	Affix handles	5
Tw	Twist	2
R	Remove hole	4
Pa	paint	6

The glass must be blown before anything else. Polishing precedes all but G and Sh; shping precedes all but G and Po. The hole must be added before it removed (!) and before the bottle is twisted. The handles go on before Tw and Pa. Once Tw, R, and Pa are completed, the project is finished.