IEOR E4007
G. Iyengar
March 10th, 2009.
IEOR E4007 Practice Midterm
Instructions
:
200pts
1.
Simple problem on LP geometry
50pts
The feasible region of the LP
max
x
1
+ 2
x
2
,
s. t.
2
x
1
+ 3
x
2
≤
20
,
3
x
1
+ 2
x
2
≤
20
,
0
≤
x
1
≤
6
,
0
≤
x
2
≤
6
.
is shown below.
x
1
x
2
x
3
x
4
x
5
(a) Compute the optimal solution of this LP. Is the optimal solution unique ? What
is the optimal value ?
10pts
(b) Suppose now the objective vector
c
θ
=
1
2
+
θ
2
−
1
Compute the range of
θ
for which the solution computed in part (a) remains
optimal.
15pts
1
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(c) The objective vector in the above LP is
c
= (1
,
2)
T
. Construct a new objective
vector
c
for which the points (4
,
4)
T
and (1
,
6)
T
are both optimal.
10pts
(d) Construct a
piecewise linear
objective function for which the points (1
,
6)
T
, (4
,
4)
T
and (6
,
1)
T
are all optimal.
15pts
2.
Problem on sensitivity analysis
65pts
A pottery manufacturer can make four kinds of dinner sets: English, Currier, Primrose,
and Bluetail. Each set uses clay, enamel, dry room time, and kiln time; and results in
a profit shown in Table 1. Primrose can be made by two different methods labeled P1
and P2 in Table 1. Currently the manufacturer is committed to producing the same
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 Summer '09
 OptimizationModelsandMethods
 Optimization, optimal solution, P1 P2, Primrose, objective vector, dry room

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