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A contractor has to supply 10000 bearings per day to an automobile manufacturer. He finds that when he starts production run, he can produce 25000 bearings per day. The cost of holding a bearing in stock for one year is $2 and the set-up cost of a production run is $180. Find the economic order quantity(EOQ). How frequently should the production run be made?
Exercise Sheet
Q1. A juice company has its products viz. canned apple and bottled juice with profit margin Rs.4
and Rs.2 respectively per unit. The following table shows the labor, equipment, and ingredients
to produce each product per unit.
Canned Apple Bottled Juice Total
Labor 2 3 12
Equipment 3.2 1 8
Ingredients 2.4 2 9
Formulate the linear programming problem (model) specifying the product mix which will
maximize the profit without exceeding the levels of resourc
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).
Solve this quadratic programming using the primal dual interior point method or the Barrier Function interior method.
Find the values of x that minimize
f(x)=0.5x2
1
+x2
2
−x1
x2
−2x1
−6x2
,
subject to the constraints
x1
≥0
x2
≥0
x1
+x2
≤2
−x1
+2x2
≤2
2x1
+x2
≤3.
Find the critical path of the following network using the EST/LSTs.
Activity Preceding Activity Duration (days)
1 - 4
2 1 7
3 1 5
4 1 6
5 2 2
6 3 3
7 5 5
8 2, 6 11
9 7, 8 7
10 3 4
11 4 3
12 9, 10, 11 4
(b). Calculate the floats of the network diagram in part (a)
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
Solve the following Transportation problem by MODIs Method
Destination
Source 1 2 3 Capacity
1 2 2 3 10
2 4 1 2 15
3 1 3 1 40
Demand 20 15 30 65
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.
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#340153 on Dec 2023