MS&E 211
Fall 2011
Linear and Nonlinear
Optimization
Oct 11, 2011
Prof. Yinyu Ye
Homework
Assignmen
t
2:
Due 6pm
Th
ursda
y
,
Oct 20
Problem 1:
Production
Managemen
t
A manager
of an oil refinery has 8 million barrels
of crude oil A and
5 million barrels
of
crude oil
B allocated for production
during the coming month.
These resources can be used
to make either
gasoline, whic
h sells for $ 38 per barrel,
or home heating
oil, which sells for
$33 per barrel.
There are three
production
processes with the following c
haracteristics:
Process 1
Process 2
Process 3
Input
crude A
Input
crude
B
Output gasoline
Output heating
oil
3
1
5
5
1
3
4
1
3
3
1
4
Cost
$51
$11
$40
All quantities
are in barrels.
For example, with the first process, 3 barrels of crude A and 5
barrels of
crude
B are used to produce 4 barrels of gasoline and 3 barrels of heating oil. The
costs in this table
refer
to
v
ariable and allocated
overhead costs, and there
are no separate
cost items for the cost of the
crudes.
(a)
First
formulate a linear programming
problem that
would help the manager maximize
net revenue o
v
er the next month.
Then use the simplex method to find an optimal
solution.
Please write down each
iteration.
(b)
Suppose that
the selling price of heating oil is sure to remain fixed over the next month,
but the selling price of gasoline may rise. Using the simplex tableau,
try to decide how high
it can go without
causing
the optimal
solution to change.
(Hint:
You w
an
t to
prev
en
t new
variable from entering the optimal
basis while
the price is
increasing.)
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Now the manager
has to consider waste disposal as well. Suppose Process 1
generates
4
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 '07
 YINYUYE
 Linear Programming, Optimization, heating oil, current basic solution

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