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Suppose that in a product-mix problem 𝒙𝟏, 𝒙𝟐 and 𝑥3 indicate the units of products 1, 2 and 3, respectively, and the Linear Programming formulation is:
Maximize Z = 20x1 + 10x2 + 15x3 Subject to: 3x1 + 2x2 + 5x3 ≤ 55 2x1 + x2 + x3 ≤ 26 x1 + x2 + 3x3 ≤ 30 5x1 + 2x2 + 4x3 ≤ 57 x1 , x2 , x3 ≥ 0
a) Use solver to find optimal solution and sensitivity report. b) Management have asked you to determine the optimal solution. Write your answer in a form of a report to be submitted to the management. c) Advice the management about objective function value corresponding to your answer in (b).
5. a. Explain the principle of Dominance giving a suitable example
b. Solve the Game graphically
1 -3
3 5
-1 6
4 1
2 2
-5 0
At a one man barber shop, customers arrive according to poison distribution with a
mean arrival rate of 5 per hour and hair cutting time was exponentially distributed
with an average hair cutting time was exponentially distributed with an average hair
cut taking 19 minutes. It is assumed that because of excellent reputation, customers
were always willing to wait. Calculate the following
a. Average number of customers in the shop and average numbers waiting for a hair
cut
b .Percentage of time arrival can walk in right without having to wait
c. The percentage of customers who have to wait before getting into the barber’s chair
Use dual Simplex method to solve the following LPP.
Max Z= -3X1-2X2
Subject to x1+x2>1
X1+X2<7
X1+2X2>10
X2<3
X1,X2>0
65
66
57
60
56
Salesman
P
Q
R
S
T
A
55 85
90
75
80
76
B
75
78
66
72
64
D
125
132
114
120
112
E
75
78
69
72
68
- 414
Find an optimal solution for maximising the total revenue.Estimated sales revenue (in 000 Rs) of 5 salesmen in 5 districts is as given below:
District
C
65
66
57
60
56
Salesman
P
Q
R
S
T
A
55 85
90
75
80
76
B
75
78
66
72
64
D
125
132
114
120
112
E
75
78
69
72
68
- 414
Find an optimal solution for maximising the total revenue.
District
C
65
66
57
60
56
Salesman
P
Q
R
S
T
A
55 85
90
75
80
76
B
75
78
66
72
64
D
125
132
114
120
112
E
75
78
69
72
68
- 414
Find an optimal solution for maximising the total revenue.
1) Complete the regularization of the following primal problem
Min Z = 15x1 + 15x2
s.t 3x1 + 2x2 > 2
7x1 + 2x2 = 6
5x1 + 7x2 < 4
x1 , x2 > 0
For model:
3x1+2x2+7x3+5x4+2x5>= 13000
2x2+x4+2x5+3x6>=20000
F(c)=0,2x1+0,1x2+0,2x3+0,3x4+0,4x5+0x6
Build a dual model, solve using the graphical method
Solve the following LPP using dual simplex method: Max Z= -3x1- x2,
Subject to: x1+x2 ≥ 1, 2x1+3x2 ≥ 2, x1,x2 ≥ 0.
#339914 on Dec 2023