Response the following:
Question . 1
A manufacturer is to market a new fertilizer which to be a mixture of two ingredients A and B. the properties of the two ingredients are given in the table:
|
|
Bone meal
|
Nitrogen
|
Lime
|
Phosphates
|
Cost(Shs)/kg
|
|
Ingredient A
|
20%
|
30%
|
40%
|
10%
|
12
|
|
Ingredient B
|
40%
|
10%
|
45%
|
5%
|
8
|
It has been decided that:
• the fertilizer will be sold in bags containing 100kgs
• it must contain at least 15% nitrogen
• it must contain at least 8% phosphates
• it must contain at least 25% bone meal
The manufacturer wishes to meet the above requirements at the minimum cost possible. Formulate a linear programming model for the problem and apply graphical method to solve it.
Question . 2
Solve the below linear program by simplex method
Minimize
Subject
Question. 3
A marketing manager has five salesmen all of different capabilities, The salesmen are to be deployed to five districts, the estimates made by the marketing manager for the sales per month (10,000 shillings) for each salesman in each district would be as follows.
District
Salesman
A B C D E
1 32 38 40 28 40
2 40 24 28 21 36
3 41 27 33 30 37
4 22 38 41 36 36
5 29 33 40 35 39
Find the assignment of salesmen to the districts that will result in maximum sales.
Question . 4
A self-service store employs one cashier at its counter. 9 customers arrive on an average every FIVE minutes while the cashiers can serve 10 customers in FIVE minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service times, find;
(i) Average number of customers in the system.
(ii) Average number of customers in the queue.
(iii) Average time a customer spends in the system.
Question . 5
A Company ltd is planning to open a new branch to grow its business. The administration is treating the move as a project to be undertaken. The following activities together with their related data have been identified.
|
Activity
|
Preceding
Activity
|
Time in Days
Optimistic Most likely Pessimistic
Time Time Time
|
|
A
B
C
D
E
F
G
H
I
J
K
|
-
A
A
B
C
D
C
F,E
G
H,I
J
|
6 9 12
6 8 10
3 7 11
12 16 20
6 11 22
12 15 24
5 7 15
4 8 12
6 8 10
14 28 48
6 6 24
|
Required:-
a) Draw a network to represent the above data
b) Determine the critical path of the project and the expected project length
c) Calculate the floats for each activity if any