EMGT 501

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EMGT 501 Mid-Term Exam Due Day Oct. 18 (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. Joyce and Marvin run a day care for
preschoolers. They are trying to decide what to
feed the children for lunches. They would like to
keep their costs down, but also need to meet the
nutritional requirements of the children. They
have already decided to go with peanut butter and
jelly sandwiches, and some combination of graham
crackers, milk, and orange juice. The nutritional
content of each food choice and its cost are
given in the table below.
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Calories from Fat
Total Calories
Vitamin C (mg)
Protein (g)
Cost ()
Food Item
Bread (1 slice)
10
70
0
3
5
Peanut butter (1tbsp)
75
100
0
4
4
Strawberry jelly (1 tbsp)
0
50
3
0
7
Graham cracker (1 cracker)
20
60
0
1
8
Milk (1 cup)
70
150
2
8
15
Juice (1 cup)
0
100
120
1
35
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The nutritional requirements are as follows. Each
child should receive between 400 and 600
calories. No more than 30 percent of the total
calories should come from fat. Each child should
consume at least 60 milligrams (mg) of vitamin C
and 12 grams (g) of protein. Furthermore, for
practical reasons, each child needs exactly 2
slices of bread (to make the sandwich), at least
twice as much peanut butter as jelly, and at
least 1 cup of liquid (milk and/or juice). Joyce
and Marvin would like to select the food choices
for each child which minimize cost while meeting
the above requirements.
(a) Formulate a linear programming model for this
problem. (b) Solve the problem.
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2. Consider the following problem.
Let and denote the slack variables for the
respective constraints. After you apply the
simplex method, a portion of the final simplex
tableau is as follows
(a) Solve the problem. (b) What is B-1 ? How
about B-1b and CBB-1b ?
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3. Alfred Lowenstein is the president of the
research division for Better health, Inc., a
major pharmaceutical company. His most important
project coming up is the development of a new
drug to combat AIDS. He has identified 10 groups
in his division which will need to carry out
different phases of this research and development
project. Referring to the work to be done by the
respective groups as activities A, B, , J, the
precedence relationships for when these groups
need to do their work are shown in the following
project network.
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A
E
I
C
F
START
Finish
D
G
J
B
H
Duration
Activity
Estimated Mean
Estimated Variance
A
4 months
5 months
B
6 months
10 months
C
4 months
8 months
D
3 months
6 months
E
8 months
12 months
F
4 months
6 months
G
3 months
5 months
H
7 months
14 months
I
5 months
8 months
J
5 months
7 months
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• Find the mean critical path for this project.
• Use this mean critical path to find the
  approximate probability that the project will be
  completed within 22 months.
• Now consider the other three paths through this
  project network. For each of these paths, find
  the approximate probability that the path will be
  completed within 22 months.
• What should Alfred tell his CEO about the
  likelihood that the drug will be ready within 22
  months?

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4. Consider the game having the following payoff
table.
Player 2
Strategy
1
2
3
4
1
5
-3
3
-1
Player 1
2
-2
4
3
2
3
3
2
-4
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(a) Formulate the problem of finding optimal
mixed strategies according to the maxmin
criterion as a linear programming problem. (b)
Use the simplex method to find these optimal
mixed strategies.