Linear Optimization (MATH 308) Assignment (Hw) #4

1. ASSIGNMENT 4
MATH 308 - LINEAR OPTIMIZATION
DUE: 6 FEBRUARY, 12 NOON.
ABRAHAM P. PUNNEN
Q1: Solve the following problem using simplex method:
Maximize 2x1 + x2 − x3
Subject to x1 + 2x2 ≤ x3 + 5
2x1 − x3 ≤ 8
x2 ≥ −3 + x1
xi ≥ 0, i = 1, 2, 3
Q2: Solve the following problem using simplex method:
Maximize 2x1 + x2
Subject to x1 + x2 + x3 ≥ 8
2x1 − x2 + 2x3 ≤ 12
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0
Q3: Consider the problem
Maximize CX
LPP:
Subject to
AX = b
Show that LPP is either infeasible, or unbounded or has a unique
optimal solution.
Q4: Show that the system
−3x1 + 2x2 + 2x3 = 8
−3x1 + 4x2 + x3 = 7
xj ≥ 0 for j = 1, 2, 3
has a feasible solution which satisfies 3x1 + 2x2 + x3 ≥ k where k
is any large number. Compute a solution to the system satisfying
3x1 + 2x2 + x3 = 10000.
Abraham P. Punnen, Department of Mathematics, Simon Fraser University
Surrey, Central City, 250-13450 102nd AV, Surrey, British Columbia,V3T 0A3,
Canada, Email: apunnen@sfu.ca
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