M.Com. DEGREE EXAMINATION, APRIL 2017
Second Semester
Commerce
QUANTITATIVE TECHNIQUES
(CBCS 2016 onwards)
Time 3 Hours Maximum 75 Marks
Part A 3 15)
Answer all questions.
All questions carry equal marks.
1. Explain the applications of duality theory.
2. We have numbered cards from 1 to 20 and picked one at
random. Find the probability that the card picked is
numbered a multiple of 2 or 5.
3. Enumerate the benefits of queuing theory.
4. State any three criteria's for decision?
5. What are the uses of Break Even Point Analysis?
Sub. Code
611702
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Part B 10 50)
Answer all questions choosing either or
6. You need to buy some filing cabinets. You know that
Cabinet X costs Rs. 10 per unit, requires six square
feet of floor space, and holds eight cubic feet of files.
Cabinet Y costs Rs. 20 per unit, requires eight
square feet of floor space, and holds twelve cubic
feet of files. You have been given Rs. 140 for this
purchase, though you don't have to spend that
much. The office has room for no more than
72 square feet of cabinets. How many of which
model should you buy, in order to maximize storage
volume?
Or
Solve the following transportation problem
Destination Available
Source 1 2 3 4
1 21 16 25 13 11
2 17 18 14 23 13
3 32 27 18 41 19
Requirement 6 10 12 15 43
7. A survey was taken on 30 classes at a school to find
the total number of left-handed students in each
class. The table below shows the results
No. of left-handed students 0 1 2 3 4 5
Frequency (No. of classes) 1 2 5 12 8 2
A Class was selected at random.
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Find the probability that the class has 2 lefthanded
students.
What is the probability that the class has at
least
3 left-handed students?
Given that the total number of students in the
30 classes is 960, find the probability that a
student randomly chosen from these 30 classes
is left-handed.
Or
Find for the following probability
distribution
X 8 12 16 20 24
1/8 1/6 3/8 1/4 1/2
8. What are the uses and limitations of simulations?
Or
Explain the significance of queuing model and its
application in business.
9. The manufacturer of a certain product is
considering the purchase of one of three different
packaging systems. The product sells for Rs. 10, and
the production cost (excluding packaging cost) is
Rs. 5 per unit. The cost data for the three packaging
systems are
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System No.: Purchase cost Variable cost per
unit of product
Scrap value
1 Rs. 100 Rs. 1.50 Rs. 10
2 Rs. 200 Rs. 1.0O Rs. 20
3 Rs. 400 Rs. 0.50 Rs. 40
All three systems last one year only and will then be sold
at the listed salvage value. The demand for the product
over the year can be regarded as a random variable with
the following probability distribution
Demand Probability
x
100 0.3
200 0.6
400 0.1
1.0
Which system should be bought?
Or
Decision Trees are excellent tools for helping you to
choose between several courses of action
Comment.
10. Two costs at Walco appear below for two months of
operations. Determine the type of cost behaviour for
each cost and briefly justify your choice.
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Cost Month Cost Units produced
Copying costs March Rs. 9,604 9,800
April Rs. 8,064 8,400
Communication Costs March Rs. 6,080 800
April Rs. 5,168 680
Or
Profit, price for target profit The Martell Company
has recently established operations in a competitive
market. Management has been aggressive in its
attempt to establish a market share. The price of
the product was set at Rs. 5 per unit, well below
that of the company's major competitors. Variable
costs were Rs. 4.50 per unit, and total fixed costs
were Rs. 600,000 during the first year.
Assume that the firm was able to sell 1 million
units in the first year. What was the pretax
profit (loss) for the year?
Assume that the variable cost per unit and
total fixed costs do not increase in the second
year. Management has been successful in
establishing its position in the market. What
price must be set to achieve a pre-tax profit of
Rs. 25,000? Assume that sales remain at
1 million units.
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Part C 10 10)
Compulsory.
11. Case study
Read the following case and answer the questions given
at the end.
Consider the transportation problem presented in the
following table
Distribution Centre
Plant D1 D2 D3 D4 Supply
P1 19 30 50 12 07
P2 70 30 40 60 10
P3 40 10 60 20 18
Requirement 5 8 7 15
Determine the optimal solution of the above problem by
applying MODI method.
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