MANAGEMENT SCIENCE homework 2

MANAGEMENT SCIENCE HOMEWORK 2
4.28
a) The sale of the tables and chairs represents the total profit. The production plan includes oak tables and chairs, cherry tables and chairs, and pine tables and chairs.
b) Labor, cherry wood, oak wood, pine wood, minimum oak tables, and minimum cherry tables are the binding constraints.
c) The range over which the unit profit for oak chairs can change without changing the production plan is between $35 and infinity.
d) The range over which the amount of available oak could range without changing the combination of binding constraints is between 900 to 2,468.93 pounds.
e) There are 0’s in the allowable increase or decrease columns.
f) It will be 0.
g) 145.31 = 41.67 oak, 75.56 cherry, and 28.08 pine

5.30

X12
X13
X14
X25
X35
X36
X41
X46
X48
X52
X53
X57
X63
X68
X75
X78
X87
X81

Car Flow
2
2
1
2
1
2
0
1
0
0
1
2
0
3
0
2
0
5

5
Max

Constraints

LHS RHS
Node 1
-1
-1
-1

1

1
0
=
0
Node 2
1

-1

1

0
=
0
Node 3
1

-1
-1

1 1

0
=
0
Node 4

1

-1
-1
-1

0
=
0
Node 5

1
1

-1
-1
-1

1

0
=
0
Node 6

1 1

-1
-1

0
=
0
Node 7

1

-1
-1
1 0
=
0
Node 8

1

1 1
-1
-1
0
=
0
Max Flow
1

2
<
2
Max Flow 1

2
<
5
Max Flow

1

1
<
1
Max Flow

1

2
<
2
Max Flow

1

1
<
2
Max Flow

1

2
<
2
Max Flow

1

0
<
1
Max Flow

1

1
<
3
Max Flow

1

0
<
4
Max Flow

1

0
<
2
Max Flow

1

1
<
1
Max Flow

1

2
<
2
Max