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DECISION ANALYSIS AND MODELING
1. Observe any government department or service process that consumes limited
resources and/or has multiple restricts, and explain what are artificial variables and why
do we need them? Also using suitable example discuss how artificial variables differ
from slack and surplus variables?
2. Obtain an initial basic feasible solution to the following transportation problem using
the Vogel’s Approximation Method.
WAREHOUSE
STORES
AVAILABILITYI II III IV
A 7 3 5 5 34
B 5 5 7 6 15
C 8 6 6 5 12
D 6 1 6 4 19
DEMAND 21 25 17 17 80
3. A processor of frozen fruits has to decide which crop to cultivate in which
geographical area. There are two strategies available: to plant apples and to plant
pomegranates. There are three possibilities of weather: perfect weather, variable
weather, and bad weather. The probability of perfect weather is 0.25, that of variable
weather is 0.50 and that of bad weather is 0.25. The outputs of the two crops, measured
in dollars, under the different conditions, are known. The utility of the firm is to be
measured by the dollar amounts as shown in the following payoff table.
ACTIONS
EVENTS
PERFECT VARIABLE BAD

2. WEATHER WEATHER WEATHER
CULTIVATE APPLES 40000 30000 20000
CULTIVATE
POMEGRANATES 70000 20000 0
a) Prepare the expected payoff table.
b) What action should the processor select?
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