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CSCI 386 Spring 2005
Final Exam (due April 30, 2005)
Please complete your exam independently and email your final exam (using .zip
format) to me. My email address is [email protected].
1. Each hour from 10 A.M. to 7 P.M., First National Bank of Gainesville
receives checks and must eventually process them. Its goal is to process
all checks the same day they are received. The bank currently has 20
check processing machines, each of which can process up to 400 checks
per hour. It takes one worker to operate each machine. This bank hires
both full-time and part-time workers. Full-time employees work 10 A.M. to
6 P.M., 11 A.M. to 7 P.M., OR noon to 8 P.M., and are paid $180 per day.
Part-time employees work either 2 P.M. to 7 P.M. OR 3 P.M. to 8 P.M.,
and are paid $90 per day. The number of checks typically received each
hour is shown in the file Final_1.xls. Formulate and solve a linear
programming model in the given Excel file to develop a work schedule that
processes all checks by 8 P.M. and minimizes daily labor costs.
2. During the next four months a consulting firm must complete three major
projects. Project 1 must be completed no more than 2 months from now
and requires 10 consultant-months of labor. Project 2 must be completed
no later than 3 months from now and requires 7 consultant-months of
labor. Project 3 must be completed no later than 4 months from now and
requires 13 consultant-months of labor. Each month, 9 consultants are
available. During a given month, no more than 5 consultants can work on
a single project. This firm wants to determine whether all three projects
can be completed on time. Using the shell provided in the file Final_2.xls,
formulate and solve an appropriate linear network model to determine if all
three projects can be completed on time
3. Five machines are available to process five jobs each day at a
manufacturing plant. The time it takes each machine to complete each of
the five jobs is given in the file Final_3.xls. If a machine is used to
process at least one job, a certain amount of time is needed to set up the
machine before processing can begin. Note that the setup time is incurred
once; that is, it is invariant with the number of jobs the given machine
handles. The setup time for each machine is also provided in Final_3.xls.
Furthermore, each machine can handle at most 2 different jobs and can
process up to 120 minutes’ worth of jobs each day. The company would
like to determine how to minimize the sum of the setup and machine
operation times needed to complete all five jobs. Using the shell provided
in Final_3.xls, formulate and solve an integer programming model to help
this company solve its problem.
4. A county is going to build two public libraries to serve its residents who live
in nine towns located within the county. Based on the results of a survey
administered to a random sample of residents living in each of the nine
towns, the county expects that each town will generate a particular
number of monthly visits to a library located in the county. These numbers
are given in the file Final_4.xls. In choosing where it should build each of
the two libraries, the county would like to minimize the total distance that
residents must travel to visit the libraries. The distance (in miles) between
each pair of towns in the county is given in the file Final_4.xls. Formulate
and solve an IP model in the given spreadsheet shell to help the county
solve its problem.
5. A recent graduate from an MBA program is trying to decide how to
allocate her available funds among three investment opportunities: stock
1, stock 2, and stock 3. From past data, the means and standard
deviations of annual returns have been estimated as shown in the file
Final_5.xls. The correlations between the annual returns of the stocks
are also listed in the given file. Suppose that for every $1 traded in any
one of these three stocks the investor must pay $0.01 in transaction costs.
Furthermore, suppose she begins with 60% of her available funds in stock
1, 20% of her funds in stock 2, and 20% of her funds in stock 3. This
investor wants to find a minimum-variance portfolio that yields an
expected annual return of at least 14%. Formulate and solve an
appropriate nonlinear optimization model in the file Final_5.xls to solve
this problem.
6. The costs of manufacturing product A, product B, or products A and B
bundled together are $60, $70, and $130, respectively.
The file
Final_6.xls lists the sizes of the three market segments for these products
and how much each of the segments is willing to pay for A alone, B alone,
or the bundle. Under the assumption that a market segment will buy the
product combination that yields the maximum nonnegative “surplus” value
and a segment will buy no product if no product has a nonnegative
surplus, determine an optimal set of product prices. Should the company
offer all products for sale?
Formulate and solve an appropriate
optimization model in the file Final_6.xls to answer this question. Your
model should include several IF statements which require the
implementation of the Evolutionary Solver.
7. A television station has commercials of the following lengths (in seconds):
15, 20, 25, 30, 40, 45, 50, and 60. The commercials must be assigned to
90-second breaks. What is the fewest number of breaks that are needed
to air all 8 of the commercials? Formulate and solve an appropriate
optimization model in the file Final_7.xls to answer this question. Your
model should include several IF statements which require the
implementation of the Evolutionary Solver.