10.
If a decision variable is not positive in the optimal
solution, its reduced cost is
a.
what its objective function value would need to be
before it could become positive.
b.
the amount its objective function value would need to
improve before it could become positive.
c.
zero.
d.
its dual price.
Quantitative Problems – (25 marks each)
11. The Prince George RCMP schedules officers for 8 hour shifts.
The shifts start at 8 am, noon, 4 pm, 8 pm, midnight and 4 am. An
officer starting one of these shifts works for the next 8 hours.
During normal weekday operations, the number of officers needed
varies on the time of day.
The staff guidelines require the
following minimum number of officers on duty:
Minimum Number Needed
Shift 1: 8 am to noon
5
Shift 2: Noon to 4 pm
6
Shift 3: 4 pm to 8 pm
10
Shift 4: 8 pm to midnight
7
Shift 5: midnight to 4 am
4
Shift 6: 4 am to 8 am
6
What is the
LP model
to determine the minimum number of officers
required to report for each shift?
Use x
i
for the decision
variables.
12. Use the following Management Scientist output to answer the
questions.
a.
Give the solution to the problem.
b.
Which constraints are binding?
c.
What would happen if the coefficient of x
1
increased by 3?
d.
What would happen if the righthand side of constraint 1
increased by 10?
LINEAR PROGRAMMING PROBLEM
MAX 31X1+35X2+32X3
S.T.
1)
3X1+5X2+2X3>90
2)
6X1+7X2+8X3<150
3)
5X1+3X2+3X3<120
Comm 251 F04
Page 3 of 6
Term Exam 1
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OPTIMAL SOLUTION
Objective Function Value =
763.333
Variable
Value
Reduced Costs



X1
13.333
0.000
X2
10.000
0.000
X3
0.000
10.889
Constraint
Slack/Surplus
Dual Prices



1
0.000
0.778
2
0.000
5.556
3
23.333
0.000
OBJECTIVE COEFFICIENT RANGES
Variable
Lower Limit
Current Value
Upper Limit




X1
30.000
31.000
No Upper Limit
X2
No Lower Limit
35.000
36.167
X3
No Lower Limit
32.000
42.889
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 Fall '12
 Herst
 Optimization, Comm, Limit of a function, objective function, 12hour clock, Term Exam

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