EMGT 501

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EMGT 501 Fall 2005 Midterm Exam Due Day Oct
17 (Noon)
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Note (a) Do not send me after copying your
computer results of QSB. Answer what are your
decision variables, formulation and solution,
only. See my HW answer on my HP. (b) Put your
mailing address so that I will be able to return
your exam result via US postal service. (c)
Answer on a PPS series of slides. (d) Do not
discuss on the exam with other students. (e)
Return your answer attached to your e-mail.
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1. Linear Programming (20) Benson Electronics
manufactures three components to produce cellular
telephones and other communication devices. In a
given production period, demand for the three
components may exceed Bensons manufacturing
capacity. In this case, the company meets demand
by purchasing the components from another
manufacturer at an increased cost per unit.
Bensons manufacturing cost per unit and
purchasing cost per unit for the three components
are as follows
Source Component 1 Component 2
Component 3 Manufacture 4.50
5.00 2.75 Purchase
6.50 8.80
7.00
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Manufacturing times in minutes for Bensons three
departments are as follows
Department Component 1
Component 2 Component 3 Production
2 3
4 Assembly
1 1.5
3 Testing and packaging 1.5
2 5
For instance, each unit of component 1 that
Benson manufactures requires 2 minutes of
production time, 1 minute of assembly time, and
1.5 minutes of testing and packaging time. For
the next production period, Benson has capacities
of 360 hours in the production department, 250
hours in the assembly department, and 300 hours
in the testing and packaging department.
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• Formulate a linear programming model that can be
  used to determine how many units of each
  component to manufacture and how many units of
  each component to purchase. Assume that component
  demands that must be satisfied are 6000 units for
  component 1, 4000 units for component 2, and 3500
  units for component 3. The objective is to
  minimize the total manufacturing and purchasing
  costs.
• What is the optimal solution? How many units of
  each component should be manufactured and how
  many units of each component should be purchased?
• Show its dual formulation
• Discuss complementary slackness condition between
  the primal and dual models.

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2. Linear Programming (15) Consider the
following problem.
Maximize
subject to
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• Solve the problem.
• What is B-1? How about B-1b and CBB-1b?
• If the right hand side is changed from (5, 4) to
  (6, 5), how is an optimal solution changed? How
  about an optimal objective value?

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3. Linear Programming (15) Suppose that in a
product-mix problem x1, x2, x3,and x4 indicate
the units of products 1,2,3, and 4, respectively,
and we have
Max
s.t.
Machine A hours
Machine B hours
Machine C hours
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• Formulate the dual model to this problem.
• Solve the dual. Use the dual solution to show
  that the profit-maximizing product mix is x10,
  x225, x3125, and x40.
• Use the dual variables to identify the machine or
  machines that are producing at maximum capacity.
  If the manager can select one machine for
  additional production capacity, which machine
  should have priority? Why?

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4. PERT/CPM (20) Building a backyard swimming
pool consists of nine major activities. The
activities and their immediate predecessors are
shown. Develop the project network.
Activity A B C D E F
G H I
Immediate Predecessor
-
-
A,B
A,B
B
C
D
D,F
E,G,H
Assume that the activity time estimates (in days)
for the swimming pool construction project are as
follows
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Activity
Optimistic
Most Probable
Pessimistic
A B C D E F G H I
5 4 6 9 4 2 8 8 4
3 2 5 7 2 1 5 6 3
6 6 7 10 6 3 10 10 5

• What is an activity schedule?
• What is a critical path?
• What is the expected time to complete the
  project?
• What is the probability that the project can be
  completed in 25 or fewer days?

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5. Inventory (15) Wilson Publishing Company
produces books for the retail market. Demand for
a current book is expected to occur at a constant
annual rate of 7200 copies. The cost of one copy
of the book is 14.50. The holding cost is based
on an 18 annual rate, and production setup costs
are 150 per setup. The equipment on which the
book is produced has an annual production volume
of 25,000 copies. Wilson has 250 working days per
year, and the lead time for a production run is
15days. Use the production lot size model to
compute the following values
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• Minimum cost production lot size
• Number of production runs per year
• Cycle time
• Length of a production run
• Maximum inventory
• Total annual cost
• Reorder point

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6. Inventory (15) A well-known manufacturer of
several brands of toothpaste uses the production
lot size model to determine production quantities
for its various products. The product known as
Extra White is currently being produced in
production lot sizes of 5000 units. The length of
the production run for this quantity is 10 days.
Because of a recent shortage of a particular raw
material, the supplier of the material announced
that a cost increase will be passed along to the
manufacturer of Extra White. Current estimates
are that the new raw material cost will increase
the manufacturing cost of the toothpaste products
by 23 per unit. What will be the effect of this
price increase on the production lot sizes for
Extra White?