Exercise 1.2 Blending Problem. Determine an optimum blend for the paint to paint a huge skyscraper. The paint
to be used can be obtained by blending four war paints and two thinners. Data on them and requirements on
the blend are given below. Formulate th
If the minimum ratio is O, the next BFS obtained by the Simplex pivot is always
same as the previous one.
T. no change in RHS. bi will be changed to b,- :i: 6 bk when kth row is the pivot
When there is more than one solut
Both primal and dual of an LP can be infeasible.
Primal infeasibfe 31m irgmsible
Maximize : a 2x; -l- X3. Minimize in :2 4y1 + 23g,
subject 0: subject to:
x1+xzs4. -y1+ 32,
xIngzx yz- 322:".
xla. x2210. MO. mail
(xii) Both primal and dual ca
[ 5 points each, 80 points total]
Consider the Standard form LP, Min cx (st) Ax = b, x2 0,
where b is anon-zero vector, A is m by n matrix, In is less than or equal to n, and the
rank(A) is In
State whether the following statements are True or False an
2015 Fall : Advanced LP Quiz 1
1. [40 points] Find an optimum solution to the following LP using Two-Phased Simplex method.
(Choose the entering variable with the most negative.)
Minimize -5x1 3x2
subjectto x1+x2 S 7
Advanced LP 2015-2 Quiz
1. [20 points] Is (3,4,1,2,0,0)T a BFS for the following? If not nd a BFS from it.
(You must use the proper way to find linear dependence relationship.)
3C] +X3 + X4 +X5+755 3"- 6
X1 +2 X2 415.763 +3 364 + X5 + x6 = 22
X1 +x2 +
3. [30 points] Consider the (LP2) which is (LPl) without the 3rd constraint.
Minz=.4x1 3x2 ,
St) 2X1 + X2 S 8
x2 3 4 (LP2)
X1,X2 2 O
(1) [10 points] From the optimum tableau for (LPl), directly obtain the optimum
revised Simplex Tableau for (LP2).
2. [30 points] Consider the following LP
Minimize x1 4x2
subjectto x1+3x2 =,3(orx2=11/3xx or x1=33x2)
x2 is 2
. . yam-V376.
x12 0, x2 IS unrestrlcted
(a) [15 points] Find an optimum solution by substituting x2 with 1 1/3 x1 and solving an LP
3. [30 points] Suppose that x* is an optimum solution to;
Minimize c x -
subject to A x = b (LP )
x Z 0 '
For some stn'ctl positi value 7, p _
(1) [15 points] Is 7 x* an optimum solution to; F9191; )( X: [3 0" cfw_8&5 LE
Minimize . c x (LP 2) g olWHUA 48
Advanced LP 2015- 3' Quiz
1. [45 points] Consider Min cx (st) Ax = b, x 2 0 where A is m by 11 matrix, In is less than
n, the rank(A) is m and b is a non-zero vector.
(1) [5 points] Explain why we may assume, without loss of generality, that b is a