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Supplement
E
Linear Programming
A. Basic Concepts
1.
Linear programming is an optimization process with several characteristics
a.
Objective function:
b.
Decision variables:
c.
Constraints:
d.
Feasible region:
e.
Parameter:
f.
Certainty:
g.
Linearity:
h.
Nonnegativity:
2.
Formulating a problem
Example E.1
a.
Step 1:
b.
Step 2:
c.
Step 3:
3.
Application E.1: Problem Formulation for Crandon Manufacturing
The Crandon Manufacturing Company produces two principal product lines. One is a
portable circular saw, and the other is a precision table saw. Two basic operations
are crucial to the output of these saws:
fabrication and assembly. The maximum
fabrication capacity is 4000 hours per month; each circular saw requires 2 hours, and
each table saw requires 1 hour. The maximum assembly capacity is 5000 hours per
month; each circular saw requires 1 hour, and each table saw requires 2 hours. The
marketing department estimates that the maximum market demand next year is 3500
saws per month for both products. The average contribution to profits and overhead
is $900 for each circular saw and $600 for each table saw.
Management wants to determine the best product mix for the next year so as to
maximize contribution to profits and overhead. Also, it is interested in the payoff of
expanding capacity or increasing market share.
SN:E1
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Supplement E: Linear Programming
Definition of Decision Variables
1
x
=
2
x
=
Formulation
Maximize:
Subject to:
B. Graphic Analysis
1.
What is the purpose of a graphic analysis?
2.
Five basic steps
a.
Plot the constraints
Example E.3
b.
Identify the feasible region
c.
Plot an objective function line
•
Corner points
Example E.4
•
Isoprofit and isocost lines
d.
Find the visual solution
e.
Find the algebraic solution
Supplement E: Linear Programming
SN:E3
Application E.2: Steps
a
and
b
for Crandon Manufacturing
Plot the constraints and shade the feasible region for Crandon Manufacturing.
Constraint
Point 1
Point 2
x
1
x
2
x
1
x
2
1
(
,
)
(
,
)
2
(
,
)
(
,
)
3
(
,
)
(
,
)
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Supplement E: Linear Programming
Application E.3: Steps
c
and
d
for Crandon Manufacturing
Plot one or more isoprofit lines.
Let
Z = $2,000,000 (arbitrary choice)
Plot
$900
x
1
+ $600
x
2
= $2,000,000
Point 1
Point 2
Profit
x
1
x
2
x
1
x
2
$2,000,000
(
,
)
(
,
)
Identify the visual solution.
Find the algebraic solution
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This note was uploaded on 12/19/2009 for the course MANAGEMENT 00123 taught by Professor Ahmed during the Spring '09 term at Albany College of Pharmacy and Health Sciences.
 Spring '09
 ahmed
 Management

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