Solutions to exam in SF1811 Optimization, June 3, 2014
1.(a)
The considered problem may be modelled as a minimum-cost network ow problem with
six nodes F1, F2, K1, K2, K3, K4, here called 1,2,3,4,5,6,
and eight arcs (F1,K1), (F1,K2), (F1,K3), (F1,K4), (F2
Exam in SF1811/SF1831/SF1841 Optimization.
Monday June 11, 2012, time: 14.0019.00
Examiner: Per Enqvist, tel. 790 62 98
Allowed utensils: Pen, paper, eraser and ruler. No calculator! A formula-sheet is
handed out.
Solution methods: If not specically state
Exam in SF1811/SF1841 Optimization.
Monday March 13, 2013, time: 8.0013.00
Examiner: Per Enqvist, tel. 790 62 98
Allowed utensils: Pen, paper, eraser and ruler. No calculator! A formula-sheet is
handed out.
Solution methods: If not specically stated in th
Exam in SF1811/SF1841 Optimization.
Wednesday May 29, 2013, time: 8.0013.00
Examiner: Per Enqvist, tel. 790 62 98
Allowed utensils: Pen, paper, eraser and ruler. No calculator! A formula-sheet is
handed out.
Solution methods: If not specically stated in t
Solution to the exam for SF1811/SF1831/SF1841
March 20, 2010
(1) The problem is in standard form
minimize c x
(LP ) :
subject to Ax = b,
x 0,
where
3 3 1 0
6 2 0 1
A=
b=
,
3
2
4
1
c=
1 .
2
,
We start with x3 and x4 as basic variables. Thus = (3, 4) an
Solutions for the exam in SF1811/SF1831/SF1841 Optimization for F.
monday June 8, 2009, time. 14.0019.00
Instructor: Per Enqvist, tel. 790 62 98
There may be alternative solutions to the problem.
1.
(a) The problem (P ) can be written on standard form
min
Exam in SF1811/SF1831/SF1841 Optimization.
Wednesday March 14, 2012, time: 14.0019.00
Examiner: Per Enqvist, tel. 790 62 98
Allowed utensils: Pen, paper, eraser and ruler. No calculator! A formula-sheet is
handed out.
Solution methods: If not specically s
Exam in SF1811/SF1831/SF1841 Optimization for F.
Tuesday August 25, 2009, kl. 14.0019.00
Instructor: Per Enqvist, tel. 790 62 98
Allowed utensils: Pen, eraser and ruler. No calculator! A formula-sheet is handed out.
Solution methods: If not specically sta
Solutions to exam in SF1811 Optimization, 18 Jan 2014
1.(a) Let x = ( x12 , x13 , x14 , x23 , x25 , x34 , x35 , x45 )T ,
where the variable xij stands for the ow in the arc from node i to node j.
Let c = ( c12 , c13 , c14 , c23 , c25 , c34 , c35 , c45 )T
Solutions for the exam in Optimization.
Wednesday May 29, 2013, time. 8.0013.00
Instructor: Per Enqvist, tel. 790 62 98
There may be alternative solutions to the problem.
1.
(a) The NW solution is given by
xij
i=1
i=2
i=3
dj
j=1 j=2 j=3
4
0
0
3
1
0
0
7
5
Solutions for the exam in SF1811/41 Optimization.
Monday June 11, 2012, tid. 14.0019.00
Examiner: Per Enqvist, tel. 790 62 98
There may be alternative solutions.
1.
(a) There are three equations that should hold if the measurements were exact.
U1 = I1 R1
Solutions for the exam in Optimization.
wednesday March 13, 2013, time. 8.0013.00
Instructor: Per Enqvist, tel. 790 62 98
There may be alternative solutions to the problem.
1.
(a) The given ow is x = (x12 , x13 , x14 , x23 , x24 , x34 ) = (6, 0, 0, 4, 0,
Solutions for the exam in Optimization.
wednesday March 14, 2012, time. 14.0019.00
Instructor: Per Enqvist, tel. 790 62 98
There may be alternative solutions to the problem.
(a) Introduce the variable xik which is one if person i is seated at table k and
Solutions to exam in SF1811 Optimization, August 18, 2014
1.(a)
The considered LP problem is a minimum cost network ow problem with three nodes:
1, 2 and 3, and six arcs: (1,2), (2,1), (1,3), (3,1), (2,3) and (3,2).
The suggested solution x = (15, 0, 10,
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out OP Ck $523045 3.0 ' V - ' om tbs), Lbs? Cm) Cm; L513? CzQT
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EXAM FOR OPTIMIZATION SF1811/SF1831/SF1841
JUNE 7, 2010
Examiner: Amol Sasane (Phone: 790 7320)
Writing time allowed: 1400-1900
Writing material: Pen or pencil, eraser and a ruler is allowed. Calculators are not
allowed! A formula sheet is provided.
Instr
EXAM FOR OPTIMIZATION SF1811/SF1831/SF1841
JUNE 8, 2011
Examiner: Amol Sasane (Phone: 790 7320)
Writing time allowed: 1400-1900
Writing material: Pen or pencil, eraser and a ruler is allowed. Calculators are not
allowed! A formula sheet is provided.
Instr
EXAM FOR OPTIMIZATION SF1811/SF1831/SF1841
MARCH 19, 2011
Examiner: Amol Sasane (Phone: 790 7320)
Writing time allowed: 0800-1300
Writing material: Pen or pencil, eraser and a ruler is allowed. Calculators are not
allowed! A formula sheet is provided.
Ins