CS330  Linear Prog. & Oper. Res.				 Dec. 2, 1998
     Quiz # 2 (Simplex Alg., Transport Prob. & Assignment)       Taha

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     fill by pen after adding enough blank space for answers.  In the former
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     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.