CS330 Linear Prog. & Oper. Res. Dec. 2, 1998
Quiz # 2 (Simplex Alg., Transport Prob. & Assignment) Taha
You may edit this quiz on-line (use an editor) or print it and
fill by pen after adding enough blank space for answers. In the former
case, you will have your own copy of the exam with answers (nice).
Please fill out your NAME below. Best wishes and prospects!
Name: ________________________ Student ID:____________________
Long Answer:
1. Take your first name and last name and concatenate with no blanks.
Convert each letter to a number (a=1,b=2,c=3,d=4,e=5,f=6,g=7,...).
Now construct the linear program where: a11= number of first letter
a12= number of second letter
a12= number of third letter
b1= number of fourth letter
a21= number of fifth letter
If you run out of letters, concatenate you full name in reverse to
lengthen (eg. "JohnDoeeoDnohJ").
Now, for your profit function, c[i]= ith digit of your Student ID #.
All constraints are less-than or equal to (ie. " <= " ).
For five points, compute the LP:
Max Z = _________ x1 + _________ x2 + _________ x3
subject to constraints:
_________ x1 + _________ x2 + _________ x3 <= ________
_________ x1 + _________ x2 + _________ x3 <= ________
_________ x1 + _________ x2 + _________ x3 <= ________
and x[i] >= 0.
Now for forty-five points run the full Simplex method, showing all
decisions, using the standard Simplex method.
Part II. Short answers: (all equal credit)
2) In the Big Syndicate (good ole B.S.), stolen cars are shipped
monthly, 61 from LA, 42 from Chicago, and 39 from NY. They are
sent to chop-shops (car disassemblers) in quiet suburbs. The
chop-shops in Oyster Bay need 55 per month, those in Anaheim
need 21, and those in Peoria need 10. If a tableau is formulated,
then:
a) a dummy supply source is required
b) a dummy demand destination is required
c) both (a) and (b) are true, i.e. need both dummies
d) neither (a) nor (b) are true
e) none of the above because the problem has no feasible
solutions, even with dummies.
3) If we number LA as 1, Chicago as 2, NY as 3, and number Oyster Bay
as 1, Anaheim 2, and Peoria 3, then the Northwest rule gives what
initial feasible solution? Give full IFS.
4) The following transportation tableau describes the costs of
transporting picnic hams from 3 Peter Parker's Premium Porkery hog
farms to the 5 Pork-mark supermarkets.
1 2 3 4 5
----+----+----+----+----+----+----+----+----+----¿ Supply
| 10 | | 12 | | 13 | | 8 | | 14 | |
1 ---- ---- ---- ---- ---- | 18
----+----|----+----|----+----|----+----|----+----´
| 15 | | 18 | | 12 | | 16 | | 19 | |
2 ---- ---- ---- ---- ---- | 22
----+----|----+----|----+----|----+----|----+----´
| 17 | | 16 | | 13 | | 14 | | 10 | |
3 ---- ---- ---- ---- ---- | 39
À---------+---------+---------+---------+---------
Demand 10 23 8 18 20
Show one full pivot of the transportation algorithm.
5) The Borg have assimilated 4 new species. Each will be assigned a new Borg
task designation with the following costs:
831 832 833 834 Species
-------------------------------------------------------------------
|
1 | $50 $50 XXX $20
Genome |
-------------------------------------------------------------------
|
2 | $70 $40 $20 $30
Meteorlg|
-------------------------------------------------------------------
|
3 | $90 $30 $50 XXX
Wave Eq.|
-------------------------------------------------------------------
|
4 | $70 $20 $60 $70
Cold Fus|
Tasks -------------------------------------------------------------------
Help parallel processing progress by giving the optimal assigment (min. cost).
Show all steps or the Borg may assimilate us to check our veracity.
Have a good day and a good weekend.