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Midterm Exam
ESI 6314 Deterministic Methods in Operations Research
ver. 1
October 21, 2009
Instructor: Dr. Vladimir L. Boginski
Research and Engineering Education Facility
University of Florida
Duration: 75 minutes
Rules: Closed books, closed notes. Calculators are allowed. It is important that you show details of
your work, where appropriate. Please return questions along with your answers.
The UF Honor Code:
"We, the members of the University of Florida community, pledge to hold ourselves and our peers to
the
highest standards of honesty and integrity."
"On my honor, I have neither given nor received unauthorized aid in doing this assignment."
NAME:
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View Full Document1.(20 points)
A post office requires different number of fulltime employees on different days of the
week. The number of fulltime employees required on each day is given in the table below. Union rules
state that each fulltime employer must work five consecutive days and then receive two days off. For
example, an employee who works Monday to Friday must be off on Saturday and Sunday. But the post
office can force employees to work one day of overtime each week. For example, an employee whose
regular shift is Monday to Friday can also be required to work on Saturday. Each employee is paid $50
a day for each of the first five days worked during a week and $62 for the overtime day (if any). The
post office wants to meet its daily requirements using only fulltime employees. Formulate an LP
whose solution will enable the post office to minimize the cost of meeting its weekly work
requirements.
Day
Number of Fulltime
Employees Required
1 = Monday
17
2 = Tuesday
13
3 = Wednesday
15
4 = Thursday
19
5 = Friday
14
6 = Saturday
16
7 = Sunday
11
Let x
1
= Number of employees who start work on Sunday and work 5 days, x
2
= Number of employees who start
work on Monday and work 5 days.
.. x
7
= Number of employees who start work on Saturday and work 5 days.
Also let o1 = Number of employees who start work on Sunday and work 6 days.
.. o7 = Number of employees who
start work on Saturday and work 6 days. Then the appropriate LP is
min z =
250(x
1
+x
2
+...x
7
) + 312(o1+o2+.
..o7)
s.t. x
1
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 Fall '09
 VLADIMIRLBOGINSKI

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