ESE304  Introduction to Optimization (Homework #3)
Fall Semester, 2010
M. Carchidi
––––––––––––––––––––––––––––––––––––
Problem #1 (30 points)
Consider the Dorian Auto problem (Example #2 in Chapter 3 of the text).
a.)
(5 points)
Find the range of values on the cost of a comedy ad for which
the current basis remains optimal.
b.)
(5 points)
Find the range of values on the cost of a football ad for which
the current basis remains optimal.
c.)
(5 points)
Find the range of values for required HIW exposures for which
the current basis remains optimal. Determine the new optimal solution if
28 +
∆
million HIW exposures are required and the range of values for
∆
for which this new optimaal solution remains optimal.
d.)
(5 points)
Find the range of values for required HIM exposures for which
the current basis remains optimal. Determine the new optimal solution if
24 +
∆
million HIW exposures are required and the range of values for
∆
for which this new optimaal solution remains optimal.
e.)
(5 points)
Find the shadow price associated with each constraint.
f.)
(5 points)
If
26
million HIW exposures are required, determine the new
optimal
z
value.
This is Problem #4 on page 231 of the text:
Operations Research
by Wayne
L. Winston.
Problem #2 (25 points)
Rad
iocomanu
facturestwotypeso
frad
ios
.Theon
lyscarceresourcethatis
needed to produce radios is labor. At present, the company has two laborers,
Laborer 1 is willing to work up to
40
hours per week and is paid
$5
per hour.
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View Full DocumentLaborer 2 will work up to
50
per week for
$6
per hour. The price as well as
the resources required to build each type of radio are given in the following
table
Radio 1
Radio 1
Radio 2
Radio 1
Price
Resource Required
Price
Resource Required
$25
Laborer 1:
1
hour
$22
Laborer 1:
2
hours
Laborer 2:
2
hours
Laborer 2:
1
hour
Raw Material Cost:
$5
Raw Material Cost:
$4
Letting
x
i
be the number of Type
i
(
i
=1
,
2
)rad
iosproducedeachweek
,
that Radioco should solve the following LP.
max
z
=3
x
1
+2
x
2
(Objective Function)
s.t.
x
1
x
2
≤
40
(Laborer 1 Constraint)
2
x
1
+
x
2
≤
50
(Laborer 2 Constraint)
x
1
,x
2
≥
0
(Sign Restrictions)
a.)
(5 points)
For what values of the price of a Type 1 radio would the current
basis remain optimal?
b.)
(5 points)
For what values of the price of a Type 2 radio would the current
basis remain optimal?
c.)
(5 points)
If laborer 1 were willing to work only
30
hours per week, then
would the current basis remain optimal? Find the new optimal solution to
the LP is the current basis does not remain optimal.
d.)
(5 points)
If laborer 2 were willing to work up to
60
hours per week, then
would the current basis remain optimal? Find the new optimal solution to
the LP is the current basis does not remain optimal.
e.)
(5 points)
Find the shadow price of each constraint.
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 Winter '11
 MichaelA.Carchidi
 Operations Research, Optimization, Harshad number, optimal solution, bushel, LINDO

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