This preview shows page 1. Sign up to view the full content.
Unformatted text preview:  2, + 8.~, 5 ?
5, + 2X. + 3X, + 4.Y, 5 I l The problem in standard form is v, X) \, Y, 2 0 EM602 I QM710 (NJ) Lecture 5
Page 53 Homework Problem 35 Homework Problem 322 (solution)
4 6!
ct== lj
2!4! Solve by MTechnique (a ) Maximize z=Zx, +3x, 5x,
(d) Minimize z = 4x,  8.5 + 3.5
subject to s, +2x, +s, =7
2.x, 5x? +.K, t 10
x,,.~*>x, 20 b) ffnd all bask solutions and their
feasibility by enumeration (see
handout)
c) Restrict to only feasible solutions and
choose the extreme point with the
optimal 2
(8,0,3,&Q, 0) L = 31 Homework Problem 322 Sensitivity Analysis (solution) (a) Masimize 2 = Z.r, +3x2  5.r,  .W?,  .W+
ct. I, +2.~~ +I, +R, = I Given an optimal simplex tableau, we
can immediately conclude:
Decision Variables and their optimal
values
Objective Function value
Scarcity or Abundance of Resources
Unit Worth I Shadow Prices I Dual
values
l 5, 5x, +.Q s, +R, = IO  x,.x2..r,_R,.s,.R. 20
r(:!+3.\f)s, (3l.\f).r,
(j+L\/).r, +.\h, = 1741
R, = 7:R? = Io..Y,..K:.X,.S, =0
. l l l Sensitivity Analysis Sensitivity Analysis (Changes in Constraint RHS) (Changes in Objective Coeffkient) How much can constraint associated with
slack (or surplus) variable SII change?
Augment RHS of resource n by amount Dn
Calculate resulting change in RHS for
each bask row (including t) according to:
New RHS = Old RHS + Dn x (Co1 entry under
sn)
Find the most restrictive range of Dn for
which the RHS of every basic row remains
,g Case 1  Change in the Objective
Coefficient for a variable that is basic
in the optimal tableau
Augment the coefffcient of Basic
variable xn by adding the amount dn
Compute the new zrow according to:
New zentry = Old zentry + dn x (Co1
entry under zn) (except, if old zsntry
was 0, leave it at 0)
Find the most restrictive range of dn for
which the zentries remain 2 0 l l l l l l EM602 I QM710 (NJ) Lecture 5
Page 54 Sensitivity Analysis Problem 339 (Changes in Objective Coefficient)
Case 2  Change in the Objective
Coefficient for a Nonbasic variable in
the optimal tableau
Augment the coefhcient of NonBasic
variable xn by adding the amount dn
Compute the new zentry for the Nonbasic variable according to:
New zentry = Old zentry  dn
Find the range of dn for which the zentry remains > 0 Consider the following LP allocation
model: l Maximize z = 3y, + 2.~~ (profit)
subject to 4x, + 3.5 < 12 (resource 1)
4x, +x2 I 8 (resource...
View
Full
Document
This document was uploaded on 03/31/2014 for the course MS 602 at NJIT.
 Spring '94
 DonaldC.Johnson

Click to edit the document details