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QUANTITATIVE METHODS
Note : Attempt only 8 Questions
- A company is deciding to choose between two mutually
exclusive projects A and B. Project A requires an initial investment of
Rs. 3,00,000 and is expected to generate cash flow of Rs. 1,50,000 per
annum for the 3 years of its life. Project B, on the other hand, requires
3,40,000, has a life of 6 years and would generate Rs., 1,00,000 every
year. Which proposal should be accepted?
- A repairman is to be hired by a company to repair
machines that break down following a Poisson process, with an average rate
of four per hour. The cost of non-productive machine time is Rs 90 per
hour. The company has the option of choosing either a fast or a slow
repairman. The fast repairman charges Rs 70 per hour and will repair
machines at an average rate of 7 per hour, while the slow repairman
charges Rs 50 per hour and will repair machines at an average rate of 6
per hour. Which repairman should be hired?
- A company has Rs 6,00,000 to invest,
and a total of three investments are available to it. If xj
rupees (in lakhs) are invested j, then a net present value (in lakhs of
rupees) of vj(xj) is obtained, where vj(xj)’s
are given below:
V1(x1)
= 7 x1 + 2
V2(x2)
= 3 x2 + 7
V3(x3)
= 4 x3 + 5
The amount placed in each investment has
to be in multiples of Rs 1 lakh only. How should the company invest Rs 6,00,000
in order to maximise the net present value obtained from the investments?
- An investor has Rs 10,000 to invest and
she has an opportunity to invest the amount in either of two investments A
or B, at the beginning of each of the following three years. The
investment A results either in a total loss of the amount invested with
probability 0.2. The conditions allow at the most one investment each year
and she can invest only Rs 10,000 each time and any additional funds
accumulated are left idle. Using dynamic programming, find the investment
policy that maximizes the expected amount of money will have after three
years.
- A company manufacturers around 150
mopeds. The daily production varies from 146 to 154 depending upon the
availability of raw materials and other working conditions.
|
Production per day
|
Probability
|
|
146
|
0.04
|
|
147
|
0.09
|
|
148
|
0.12
|
|
149
|
0.14
|
|
150
|
0.11
|
|
151
|
0.10
|
|
152
|
0.20
|
|
153
|
0.12
|
|
154
|
0.08
|
The finished mopeds are
transported in a specially arranged lorry accommodating only 150 mopeds. Using
following random numbers 80,81,76,74,64,43,18,26,10,12,65,68,69,61,57,
stimulate the process to find out:
(i)
What
will be the average number of mopeds waiting in the factory?
(ii)
What
will be the average number of empty spaces on the lorry?
- The XYZ company is considering
whether or not to invest Rs 1,20,000 in an investment proposal to add a
new product to its existing range. The management forecasts that the new
plant will generate incremental net cash flows, each of which is assumed
to be normally distributed random variable with following parameters.
|
Year
|
Expected
Value (Rs)
|
Standard
Deviation (Rs)
|
|
1
|
44,000
|
5,800
|
|
2
|
40,000
|
5,600
|
|
3
|
40,000
|
6,000
|
|
4
|
35,000
|
5,000
|
|
5
|
30,000
|
4,000
|
Using the discount rate of 10
% determine:
(a) the mean of the present value
distribution and its standard deviation,
(b) the probability that the investment shall
have a negative NPV,
(c) whether the project should be undertaken
if the management has laid down that no project be undertaken unless it has at
least 70 % chance of giving an NPV at least equal to Rs 25,000.
- Differentiate marginal and
average revenue.
- What
are reasons for conducting business research?
- Explain
the consumer surplus and producer surplus with an example.
- The
company had declared that the sales of Horlicks has increased by 10% after
the advertisement. You assigned to measure the impact of advertisement
among horlics users. Try to develop the questionnaire for measuring impact
of advertisement on horlicks among the users.
Assignment Solutions, Case study Answer sheets
Project Report and Thesis - Contact
ARAVIND – 09901366442 – 09902787224
