B.C.A. DEGREE EXAMINATION – COMPUTER APPLICATIONS
FOURTH SEMESTER – APRIL 2008
CA 4203 / 4201 - RESOURCE MANAGEMENT TECHNIQUES
Date : 25-04-08
Time : 9:00 - 12:00
Dept. No. Max. : 100 Marks
DC 6
SECTION-A
ANSWER ALL THE QUESTIONS:
1.
What is a slack variable?
5.
What is total elapsed time?
6.
Differentiate optimistic and pessimistic time estimate.
(10x2=20)
2.
Define degenerate solution.
3.
Write down the conditions for solving transportation problem.
4.
Write down the route condition for the traveling salesman problem.
7. Write a note on normal and crash time.
8. What is Reorder level?
9. What is safety stock?
10. What present worth factor?
SECTION-B
ANSWER ALL THE QUESTIONS : (5x8=40)
11. a) A company has three operational departments (weaving, processing and Packing) with capacity to produce three different types of clothes namely suiting, shirting and woolens yielding a profit of
Rs.2, Rs.4 and Rs.3 per metre respectively. One metre of suiting requires 3 minutes in weaving, 2 minutes in processing and 1 minute in packing. Similarly one metre of shirting requires 4 minutes in weaving, 1 minute in processing and 3 minutes in packing. One metre of woolen requires 3 minutes in each department. In a week total run time of each department is 60, 40 and 80 hours for weaving, processing and packing respectively. Formulate the linear programming problem to find the product mix to maximize the profit.
(OR)
b) Use graphical method to solve the following L.P.P:
Maximize Z = 4x
1
+3x
2
subject to the constraints :
2x
1
+x
2
≤1,000
x
1
+x
2
≤ 800
x
1
≤ 400
x
2
≤ 700
x
1
,x
2
≥ 0
12. a) A marketing manager has 5 salesmen and 5 sales districts. Considering the capabilities of the salesman and the nature of districts, the marketing manager estimates that sales per month (in hundred rupees) for each salesman in each district would be as follows:
Salesman Sales District
1
2
3
4
A
32
40
41
22
B
38
24
27
38
C
40
28
33
41
D
28
21
30
36
5 29 33 40 35 39
What is the maximum sales that may be expected if an optimum assignment is made?
(OR)
b) Given the following data:
Job : 1 2 3 4
Machine A : 12 10 9 14
Machine B : 7 6 6 5
Machine C : 6 5 6 4
5
7
4
2
6
9
4
4
E
40
36
37
36
1

Order of Processing: A C B
Sequence Suggested: Jobs 5, 3, 6,2,1,4
(i) Determine the total elapsed time for the sequence suggested.
(ii) Is the given sequence optimal?
(iii)
If your answer to (ii) is ‘NO’ determine the optimal sequence and the total elapsed time associated with it.
13. a) A machine shop has four machines A, B, C and D. Two jobs must be processed through each of these machines. The time (in hours) taken on each of the machines and the necessary sequence of jobs through the shop are given bellow:
Job1 Sequence time
A
2
D
B
4
B Job2 Sequence time 6 4
Use graphic method to obtain the total minimum elapsed time.
(OR) b) (i) Write down the difference between PERT & CPM. (4)
(ii) Define the following terms:
a)dummy activity b) total float (4)
C
5
A
2
D
1
C
3
14. a) The annual demand for an item is 3200 units. The unit cost is Rs. 6/- and inventory carrying charges 25% per annum. If the cost of one procurement is Rs. 150/- determine (i) Economic order quality (ii) time between two consecutive orders (iii) number of order per year (iv) the optimal total cost.
(OR)
b) A dealer supplies you the following information with regard to a product dealt in by him:
Annual demand : 10,000 units; ordering cost :Rs.10 per order;price:Rs.20 per unit.
Inventory carrying cost:20% of the value of inventory per year.
The dealer is considering the possibility of allowing some back-order(stock-out) to occur. He has estimated that the annual cost of back-ordering will be 25% of the value of inventory.
(i) What should be the optimum number of units of the product he should by in one lot?
(ii) What quantity of the product should be allowed to be back-ordered, if any?
(iii) What would be the maximum quantity of inventory at any time of the year?
(iv)Would you recommend to allow back-ordering? If so, what would be the annual cost saving by adopting the policy of back-ordering?
15. a) Find the optimum order quantity for a product for which the price breaks are as follows:
Quantity
0 ≤ Q1 < 100
100 ≤ Q2 < 200
200 ≤ Q3
Purchasing cost per unit
20
18
16
The monthly demand for the product is 400 units. The storage cost is 20% of the
unit cost of the product and the cost of ordering is Rs.25 per month.
(OR) b) A Taxi owner estimates from his past records that the cost per year
for operating a taxi whose purchase price when new is Rs.60,000 are
given below.
Age : 1 2 3 4 5
Operating cost : 10,000 12,000 15,000 18,000 20,000
After 5 years the operating cost is Rs.6000 K where K=6,7,8,9,10 ( K is the age in year). If the resale value decreases by 10% of the purchase price each year What is the best replacement policy?
SECTION-C
ANSWER ANY TWO QUESTIONS : (2X20=40)
16. i) Solve the following L.P.P by simplex method
Maximize Z = 2x
1
+3x
2
subject to the constraints:
x
1
+3x
2
≤6 (10)
3x
1
+2x
2
≤ 6
x
1
,x
2
≥ 0
ii) A company has 3 plants at located A, B & C. Supply warehouses located
at D,E, F,G & H. Monthly plant capacity are 800, 500 & 900 units
respectively. Monthly warehouses requirements are 400,400,500,400 &
2

800 respectively. Unit transportation costs are given below:
Warehouses
D E F
A 5 8 6
G
6
H
3 (10)
Plants B 4 7
C 8 4
7
6
6
6
6
3
Determine an optimum distribution for a company in order to minimize the
total transportation cost.
17. (i) Given the following information:
Activity a m b
1-2
1-6
2-3
2-4
3-5
4-5
6-7
5-8
7-8
3
2
6
2
5
3
3
1
4
6
5
12
5
11
6
9
4
19
15
14
30
8
17
15
27
7
28 i) Draw the Project Network ii) Find the length and variance of each activity.
(10) iii) Find the critical path. iv) Find the length and variance of the critical path. v) What is the probability of completing the project in 41 days? vi) What is the probability of completing the project in 35 days?
(ii) A small Project consisting of 13 activities have the following information
regarding duration of the various activities. (10)
Operations Durations
1,2 8
1,3
1,5
2,4
2,5
2,6
3,4
3,8
4,6
5,6
5
7
3
5
12
0
9
7
4
5,7
6,7
2
6
7,8
(i) Draw the CPM Network
10
(ii) Perform all the CPM calculation and present them in a standard tabular form.
18. (i) Machine A cost Rs.9000. Annual operating costs are Rs.200 for the first year, and then increase by Rs.2000 every year. Determine the best age at which to replace the machine .If the optimum replacement policy is followed, what will be the average yearly cost of owning and operating the machine?
Machine B cost Rs.10000. Annual operating costs are Rs.400 for the first year and then increase by Rs.800 every year. You now have a machine of type A which is one year old. Should you replace it with B, if so when? (10)
(ii) The cost of a new machine is Rs.5000. The maintenance cost of n th year is given by Cn = 500(n-
1); n=1, 2, 3….. . Suppose that the discount rate per year is 0.05 .After how many years it will be economical to replace the machine by a new one? (10)
3