University of Delhi 2010-1st Year M.Com Commerce QUANTITATIVE TECHNIQUES OF BUSINESS ISIONS UNIVERSITY - Question Paper
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[This question paper contains 24 printed pages ]
Your Roll No
M.Com./I
6450C
Course 104 - QUANTITATIVE TECHNIQUES OF BUSINESS DECISIONS (OCAdmissions of 2003 and before)
Time 3 Hours Wl : 3
Maximum Marks 75
Tplfa1 : 75
(Write your Roll No on the top immediately on receipt of this question paper )
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Note : Answers may be written either in English or m Hindi, but the same medium should be used throughout the paper.
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Attempt all questions All the parts of a question should be answered together and in the given order
6450C ( 2 )
1 (a) What is the scope of linear programming in solving management problems 9 Explain the implications of the following assumptions of LP model (i) Linearity of objective function and constraints (u) Continuous variable (in) Certainty
(b) Following information relates to availability of media, number of families expected to be reached with each alternative, cost per advertisement, the maximum availability of each medium and the expected exposure of each one (measured as the relative value of one advertisement m each of the medial
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Other information and requirements are |
(a) The advertising budget is Rs 70,000
( 3 ) 6450C
(b) At least 40,000 families should be covered (The families receiving messages could be common But, a family receiving three messages, for example, would be taken equivalent to three)
(c) At least two insertions be given m Sunday edition but not more than 4 ads should be given on T V Formulate the given problem as linear programming problem for maximisation of expected exposure
Or
(a) Formulate the following as linear programming problem
A trucking company with Rs 40,00,000 to spend on new equipment is contemplating three types of vehicles Vehicle A has 10 tonne pay-load and is expected to average 35 km per hour It costs Rs
80.000 Vehicle B has a 20 tonne pay-load and is expected to average 30 km per hour It costs Rs
1.30.000 Vehicle C is a modified form of B, it carries sleeping quarter for one dnver, and this reduces its capacity to 18 tonne and raises the cost to Rs
1.50.000 Vehicle A requires a crew of one man, and if driven on three shifts per day, could be run for an average of 18 hours per day Vehicle B and C require a crew of two men each Whereas B would be driven 18 hours per day with three shifts, C could
6450C ( 4 )
average 21 hours per day The company has 150 drivers available each day and would find it very difficult to obtain further crews Maintenance facilities are such that the total number of vehicles must not exceed 30 How many vehicles of each type should be purchased if the company wishes to maximise its capacity in tonne-km per day
(b) Find the graphical solution to the following linear programming problem Maximize Z = 10a + 8v sub to
2x + y<2Q x + 3y<30 x-2y> -15 Non Neg x, y > 0 Is the solution unique9 Give reason
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( 5 ) 6450C
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6450C ( 6 )
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( 7 ) 6450C
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2x+ v<20 x + 3 v < 30 x-2 v> -15
Non Neg x, j; > 0
(a) A firm uses three machines in the manufacture of three products Each unit of product A requires 3 hours on machine 1, 2 hours on machine II and one hour on machine III Each unit of product B requires 4 hours on machine I, one hour on machine
II and 3 hours on machine III, while each unit of product C requires 2 hours on each of the three machines The contribution margin of the three products is Rs 30, Rs 40 and Rs 35 per unit respectively The machine hours available on three machines are 90, 54 and 93 respectively (i) Formulate the above problem as linear programming problem
6450C ( 8 )
(u) Obtain optimum solution to the problem use simplex method (m) What are the shadow pnces of the resources7 (iv) Is the optimal solution degenerate7 Or
Explain the problem situation involving (1) Unbounded solution,
(u) Infeasible solution,
(in) Multiple optimum solution, and (iv) Degeneracy
How can each of these be identified while applying simplex algorithm
(b) Write the dual of the following LPP
Max 2 = 4jcj + 52 - 3x3
sub to 2x, + 3x2 + Xj 18
5xj +4jc2 -x3 >12 6x, - 3x2 + 2xj = 10
Non Neg jCpX20, x unrestricted in sign
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( 9 ) 6450C
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6450C ( 10 )
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3 A cement company has three factories manufactunng cement which is then transported to four distribution centres The quantity of monthly production of each factory, the demand of each distribution centre and the associated transportation cost per quintal are given as follows
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Distribution Centres |
Monthly | ||||
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Factories |
P |
Q |
R |
S |
Production (in Units) |
|
A |
10 |
8 |
5 |
4 |
7,000 |
|
B |
7 |
9 |
15 |
8 |
8,000 |
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C |
6 |
10 |
14 |
8 |
10,000 |
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Monthly Demand (in Units) |
6,000 |
6,000 |
8,000 |
5,000 | |
Use least cost method to obtain initial solution (i) Find the optimum transportation schedule
( 11 ) 6450C
(u) Is there any other possible transportation schedule ?
Give reason (ui) Is the solutions degenerate7 Give reason
Or
(a) A company has four sales representatives who are to be assigned to four different sales territories The
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monthly sales increase estimated for each sales representative for different sales territories (in lakh of rupees) are shown m the following table | |||||||||||||||||||||||||||||
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Suggest optimal assignment and the total maximum sales increase per month
(b) A transportation problem has four sources of supplies and five requirement destinations For the given cost of shipping per unit from one source to a particular destination shown in the following table, find initial basic feasible solution using Vogel's Approximation Method (VAM)
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( 13 ) 6450C
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6450C ( 14 )
4 (a) Find the sequence that minimises the total elapsed
time required (T) in completing the following jobs Each job is processed in the order ABC Also calculate T
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Job |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
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Machine A |
10 |
8 |
12 |
6 |
9 |
11 |
9 |
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Machine B |
6 |
4 |
6 |
5 |
3 |
4 |
2 |
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Machine C |
8 |
7 |
5 |
9 |
10 |
6 |
5 |
(b) A manufacturing company has determined from an analysis of its data the following information (1) Demand9,000 units per annum uniformly
distributed over the year (n) Cost priceRs 2 per unit (m) Ordering CostRs 40 per order (iv) Inventory Carrying9% of inventory value charge
Lead time is uniform and equals 8 working days, and total working days m a year are 300 Determine the following on the basis of the information given above
(a) The economic order quantity (EOQ)
(b) Optimum number of orders per annum
(c) Total inventory cost associated with EOQ
(d) Re-order level
( 15 ) 6450C
(e) Amount of saving that become possible by switching to the policy of ordering EOQ determined m (a) above from the present policy of ordering the requirements three times a year
(f) The increase in total cost associated with ordering (1) 20% more, and (n) 40% less than the EOQ
Or
(a) The purchasing manager of a distillery company is considering three sources of supply for oak barrels The first supplier offers any quantity of barrels at Rs 150 each The second supplier offers barrels in lots of 150 or more at Rs 125 per barrel The third supplier offers barrels in lots of 250 or more at Rs 100 each The distillery uses 1,500 barrels a year at constant rate Carrying cost are 40 percent, and it costs the purchasing agent Rs 400 to place an order Calculate the total annual cost for the orders placed to the probable suppliers, and find out the supplier to whom orders should be placed
(b) What is a queuing problem9 What are the basic characteristics of a queuing system Calculate the arrival and service rates at the certain petrol pump where customers arrive in a Poisson process with an average time of five minute between successive arrivals The time taken at the petrol pump to serve
[P T O
customers follows exponential distribution with an average of two minutes
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( 17 ) 6450C
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6450C ( 18 )
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5 (a) A project consists of nine variables whose time estimates (in weeks) and other characteristics are given below
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Activity |
Preceding Activity |
Time Estimates (weeks) | ||
|
Most optimistic |
Most likely |
Most pessimistic | ||
|
A |
2 |
4 |
6 | |
|
B |
6 |
6 |
6 | |
|
C |
6 |
12 |
24 | |
|
D |
A |
2 |
5 |
8 |
|
E |
A |
11 |
14 |
23 |
|
F |
iB> D |
8 |
10 |
12 |
|
G |
B, D |
3 |
6 |
9 |
|
H |
C, F |
9 |
15 |
27 |
|
I |
E |
4 |
10 |
16 |
(I) Show the PERT network for the project
(II) Identify the critical activities
(III) What is the expected project completion time and its variance9
(iv) What is the probability of completing the project one week before the expected time9
(v) If the project is required to be completed by December 31 of any particular year, and the manager wants to be 95% sure of meeting the deadline, when should be start the project work9
(b) A firm has a machine whose purchase price is Rs
20,000 Its maintenance cost and resale price at the
end of the years are given as follows Year 1 2 3 4 5 6
Maintenance 1
Cost 1,500 1,700 2,000 2,500 3,500 5,500
Resale Price 17,000 15,300 14,000 12,000 8,000 3,000
6450C ( 20 )
Obtain the economic life of the machine and the minimum average cost Or
(a) Explain the concept of resource levelling How it. is different from resource allocation problem9
(b) How do you differentiate between NPV and IRR methods of evaluating investment proposals9 Do they always lead to same conclusion with respect to
(1) accept/reject decision for different proposals, and
(u) ranking of various proposals that are mutually exclusive m nature
(c) In a small town there are only two stores that handle sundry goods-ABC and XYZ The total number of customers is equally divided between the two, because price and quality of goods sold are equal Both stores have good reputation in the community, and they render equally good customer service Assume that a gam of customer by ABC is a loss to XYZ and vice-versa Both stores plan to run annual pre-Diwali sales dunng the first week of November Sales are advertised through a local newspaper, radio and television media With the aid of an advertising firm, store ABC constructed the
( 21 ) 6450C
game matrix given below [Figures m the table represent gam or loss of customers]
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Strategy of Strategy of XYZ | ||||||||||||||||
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Determine optimal strategies and worth of such strategies for both ABC and XYZ
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6450C ( 22 )
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100
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Attachment: |
| Earning: Approval pending. |
