Homework 6:
Economic Analysis III, IV
Due noon Wednesday 10/30
CSCI 510, Fall 2019
30 points
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Complete the following questions. Show all of your work (it helps get partial
credit).
1. (10 points) Suppose you are the manager of Galactic Software, Inc., which has
5 analysts, 12 programmers, and access to 16 hours per day of computer time
over the next year. You are offered the opportunity to develop a number of
similar simulation models and operating system utilities for a large computer
vendor. Each model you develop will require 1 analyst, 1 programmer, and 4
hours per day of computer time, and will yield you a profit of $25K. Each utility
you develop will require 1 analyst, 3 programmers, and 2 hours per day of
computer time, and will yield a profit of $15K. Your decision problem (which is a
linear programming problem) is to choose the number of models m and the
number of utilities u to develop, in order to maximize total profit, subject to the
constraints imposed by your available number of analysts, programmers, and
hours per day of computer time. Graph the constraints. Indicate the feasible
region. Also show some contours of constant profit (“isoquants”) ($K is not
shown)
25m + 15u = a constant;
show at least one isoquant that is outside the feasible region, at least one
isoquant that is largely inside the feasible region, and the isoquant that yields
the optimal solution (it will intersect the feasible region at a corner with m and u
being integers).
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State the optimal solution (a value of m and a value of u) and the optimal profit.
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(Generally, it’s most efficient to do the graphing manually, with a ruler and
perhaps graph paper.)
x1 model: 1analyst, 1programmer, 4 hr/day computer time.
x2 utility: 1 analyst, 3 programmers, 2 hr/day computer time.
Overall limits: 5 analysts; 12 programmers; 16 hr/day computer time.
Reality limits: Can’t have negative number of projects.
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Reality:
o x1 >= 0
o x2 >= 0
Analysts:
o x1 + x2 <= 5
Programmers:
o x1 + 3 * x2 <= 12
Computer time:
o 4 * x1 + 2 * x2 <= 16
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Optimal profit: m=3, n=2, profits $105K.
sh
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2. (10 points) Suppose you have a choice of two software programs to develop
for a term project in a class: a relatively hard one and a relatively easy one. The
payoff matrix below indicates your course grade as a function of the alternative
you pick and the state of nature ("Unfavorable" means that the hard project was
too hard to do well).
Alternativ
e
Hard
State of Nature
Favorable
Unfavorable
A
C+
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Easy
B
B
Determine your best alternative under a) the maximin rule, b) the maximax
rule, and
c) the Laplace rule, using the following scale to compute expected
values:
6
5
4
3
2
1
0
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A
AB+
B
BC+
C
d) Also compute the breakeven point.
1. Easy, lowest of easy is B and is greater than Hard’s lowest which
is C+.
2. Hard highest of hard is A, and is greater than Easy’s highest
which is B.
3. Hard. Because 3.5 is greater than 3.
Do not:6*0.5+1*0.5=3.5
Develop:3*0.5+3*0.5=3
4. Breakeven point:
P*6+(1-p)*1=p*3+(1-p)*3
P(on time)=0.4
p>0.4 choose hard
p<0.4 choose easy
State of Nature
Alternative
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3. (10 points) Recall TPS Decision Problem 7 from EC-11. Its payoff matrix is:
Bold (BB)
Conservative (BC)
Favorable
250
Unfavorable
-50
50
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50
Compute the resulting (EV)no info, (EV)perfect info, and EVPI. Assume P(SS) = P(SF) =
0.5.
Also complete the table below by providing the correct values for the 15 cells
with “?”. (The P(IB), P(IC), P(SS|IB), and P(SF|IB) columns are optional, but may
be useful to you. In any case, these columns will not be graded.)
Estimated
P(IB|SF)
P(IB|SS)
0
10
20
35
50
0.30
0.20
0.10
0.00
0.80
0.90
0.95
1.00
P(IB)
P(IC)
P(SS|
IB)
P(SF|IB)
Expected
Value
Net
Expected
Value
of
Prototype
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
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Cost
of
Prototype
Expected
Value
of
Information
(Caution: You might think that slide 19 from EC-11 would be a solution,
but it isn’t.)
Answer:
P(SS) = P(SF) = 0.5.
(EV)no info = E(BC)no info = P(SS) * 250 + P(SF) * (-50)
= 0.5 * 250 + 0.5 * (-50)
= 100
(EV)perfect info = P(SS) * 250 + P(SF) * 50
= 0.5 * 250 + 0.5 * 50
= 150 (because 250 is the best payoff in the SS case, and 50 in
the SF case).
EVPI = (EV)perfect info - (EV)no info = 150-100=50
Estimated
Expec-ted
Value
Expected Value
of Information
Net
Expected
Value of
Prototype
$100k
$0k
$0k
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P(IB|
SF)
P(IB|
SS)
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Cost
of
Prot
otype
0
-
10
20
0.30
0.20
P(IB)
P(IC)
P(SS|
IB)
P(SF|
IB)
-
0.5
0.80 5
0.90 0.5
0.45
0.4
0.73
0.82
0.27
0.18
$115.45k $15.45k
$130.3k $30.3k
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$5.45k
$10.3k
35
50
0.10
0.00
5
0.5
0.95 25
1.00 0.5
5
0.4
75
0.5
0.90
5
1.00
0.09
5
0.00
$140.03
75k
$150k
$40.037 $5.037
5k
5k
$50k
$0
Grading Notes
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To earn points, must show the equations used and show your
work in obtaining the answers!
Be sure to specify the units of your values, where they apply
(such as, PM, $, K, etc.).
Remember to maintain 3+ significant digits throughout the
calculations and in the final answers to earn points.
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