1
Business Decision Analysis
Name - Atul Joshi
SI- 2018070974
Put Unit # 7
BUSI 2013 Business Decision Analysis
Yorkville University – Vancouver Campus
Instructor: Dr. Christian Tabi Amponsah
Submission Date :
5/5 2019
Table of Contents

1
Abstract

2
Introduction Starts here but don’t write the word introduction.
Type equation here.

3
Problem 1
Answer 1
A)
Max
30
x
1
+ 25
x
2
s.t.
3
x
1
+ 1.5
x
2
≤
400
1.5
x
1
+ 2
x
2
≤
250
1
x
1
+ 1
x
2
≤
150
x
1
,
x
2
≥
0 and
x
2
integer
This Linear program is a mixed integer linear program because mixed integer linear program is a
linear program in which some but not necessarily all, variable are required to be an integer. This
linear program requires
x
2
to
be an integer but
x
1
can assume any positive value.
LP relaxation is the linear program that result from dropping the integer requirements for the
variables in an integer lines
Max
30
x
1
+ 25
x
2
s.t.
3
x
1
+ 1.5
x
2
≤
400
1.5
x
1
+ 2
x
2
≤
250
1
x
1
+ 1
x
2
≤
150
x
1
,
x
2
≥
0

4
B)
Min
3
x
1
+ 4
x
2
s.t
2
x
1
+ 4
≥
8
2
x
1
+ 6
≥
12
x
1
,
x
2
≥
0 and integer
This linear program is a all integer liner program because an all integer linear program is a linear
program with the additional requirement that all variable must be integer. This linear program
requires
x
1
and
x
2
to be an integers.
LP relaxation is the linear program that results from dropping the integer requirements for the
variables in an integer linear program.
Min
3
x
1
+ 4
x
2
s.t
2
x
1
+ 4
x
2
≥
8
2
x
1
+ 6
x
2
≥
12
x
1
,
x
2
≥
0
Problem 3
Answer
3
Max
1
x
1
+ 1
x
2
s.t
4
x
1
+ 6
x
2
≤
22
1
x
1
+ 5
x
2
≤
15
2
x
1
+ 1
x
2
≤
9

5
x
1
,
x
2
≥
0 and integer
Graphical representation of the constraint
16
14
12
10
(0,9)
8
2
x
1
+ 1
x
2
≤
9
Feasible region
6
(0,5)
4
x
1
+ 6
x
2
≤
22
4
(0,3.67)
1
x
1
+ 5
x
2
≤
15
2
(4.5,0)
(5.5,0)
(15,0)
0
2
4
6
8
10
12
14
16
B) Solving the LP relaxation

6
Problem 3
X1
X2
Constrai
n
4
6
22
1
5
15
2
1
9
Model
Max
5
X1
X2
Optimal
Solution
4
1
Constraint
LHS
RHS
1
22
<=
22
2
9
<=
15
3
9
<=
9
10
(0,9)
8
2
x
1
+ 1
x
2
≤
9
Feasible region
6
(0,5)
4
x
1
+ 6
x
2
≤
22
(4,1) (optimal point)
4
(0,3.67)
1
x
1
+ 5
x
2
≤
15
2
(4.5,0)
(5.5,0)
(15,0)
0
2
4
6
8
10
12

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