INDIVIDUAL ASSIGNMENT FOR QUANTITATIVE ANALYSIS FOR
DECISION MAKING
1. Consider Special cases in linear programming problem.
 Write Detailed notes for each
 Explain mechanisms of identifications of special case
 Give at least one example for each special case
 Consider both maximization and minimization objective functions.
2. A car rental company has one car at each of five depots a, b, c, d and e. A customer in each
of the five towns A, B, C, D and E requires a car. The distance in (in kilometers) between
the depots and towns where the customers are, is given in the following distance matrix:
Depots
Towns
a
b
C
d
e
A
160
130
175
190
200
B
135
120
130
160
175
C
140
110
155
170
185
D
50
50
90
80
110
E
55
35
70
80
105
How should the cars be assigned to the customers so as to minimize the distance traveled?
3. An airline company has drawn up a new flight schedule involving five flights. To assist
in allocating five pilots to the flights, it has asked them to state their preference scores by
giving each flight a number out of 10 .The higher the number , the greater is the preference.
Certain of these flights are unsuited to some pilots owing to domestic reasons. These have
been marked with a X. What should be the allocation of the pilots to flights in order to
meet as many performances as possible? (Hint: The problem is to maximize the total
preference score).
Pilot
Flight number
a
b
C
d
e
A
8
2
X
5
4
B
10
9
2
8
4
C
5
4
9
6
X
D
3
6
2
8
7
E
5
6
10
4
3
4. A workshop prepared two articles A and B .The time required at different stages and
profit per unit are shown below. Formulate the LP model
Work
Cutting
Machine
Packing
Profit per unit($)
A
2
1
1
50
B
1
2
0.5
60
Total capacity
80
100
50
center product
5. A farmer use his land to produce rice and wheat .Labor required per acre and profit per
acre given below. Formulate the LP model
Labor per
Profit per
acre(hrs)
acre($)
X
2
100
Wheat
Y
3/2
60
Total
200
300
Community
Allocated area in acres
Rice
6. A company produces two types of container K and L. Each product has resource
requirements and profit contribution as follows:
In addition, because of demand, a maximum of 4 units of container K units of be produced. Obtain
the optimal solution using graphical method.
Resource
K
L
Total resource available
Material(Kg/unit)
1
2
10Kg
Labor(Hr/unit)
6
6
36Hr
Profit
4
5
7. Personal Mini Warehouses is planning to expand its successful Orlando business into
Tampa. In doing so, the company must determine how many storage rooms of each size
to build. Its objective and constrains follow:
Maximize monthly earnings= 50X1 +20X2
Subject to: 2X1+4X2<400 (Advertising budget available)
100X1 +50X2<8,000(Square footage required)
X1
<60(Rental limit expected)
X1 X2>0
Where: X1=Number of large spaces developed
X2=Number of large spaces developed
(Use both Graphical and Simplex Methods)
8. The 3rd and final simplex tableau for the LPP is:
Max.Z= 200x1+200x2
St:
2x1+x2 < 8
x1+3x2 <9
x1, x2 > 0
Cj
$200
$200
$0
$0
SV
X1
X2
S1
S2
Q
$200
X1
1
0
3/5
-1/5
3
250
X2
0
1
-1/5
Zj
$200
$200
0
Cj - Zj
0
2/5
2
$80
$40
$1,000
-$80
-$40
What are the solutions of the dual variables, u1, u2 and u3? What is the optimal dual cost?