Data Model Application -RM - II - Rinku Jain
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K. J. SOMAIYA INSTITUTE OF MANAGEMENT STUDIES AND RESEARCH,
Vidyavihar, Mumbai- 400077
Program: PGDM-RM(Batch2013-15), Trim-II
Subject: Data Model Applications
(End Term Examination)
Maximum Marks: 50
Duration: 3 hrs. Date: 30
th
Jan, 2014
Instructions 1. This exam will be conducted in the computer lab. All answers are to be written in the
answer sheet. Use Excel where required.
2. Question No 1 is compulsory.
3. Attempt any four questions from the remaining five questions.
QUESTION 1
(10)
The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest
$250,000 for her money obtained recently through the sale of land holdings in Ohio. The client
has a good deal of trust in the investment house, but she also has her own ideas about the
distribution about the funds being invested. In particular, she requests that the firm selects
whatever stocks and bonds they believe are well rated, but within the following guidelines:
(a)
Municipal bonds should constitute at least 20% of the investment.
(b) At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufactures.
(c)
No more than 50% of the amount invested in municipal bonds should be placed in high risk, high-yield nursing home stock.
Subject to these restraints, the client’s goal is to maximize projected return on investments. The analyst at Heinlein and Krampf aware of these guidelines, prepare a list of high quality stocks and bonds and their corresponding rates of return:
Investment
Projected Rate of Return (%)
Los Angeles municipal Bonds
5.3
Thompson Electronics, Inc.
6.8
United Aerospace Corp.
4.9
Palmer Drugs
8.4
Happy Days Nursing Homes
11.8
Questions:
(a)
Formulate the portfolio selection problem using LP.
(b) Solve this problem and interpret.
QUESTION 2
(10)
A company has four factories situated in four different locations in the country and four sales
agencies located in four other locations in the country. The cost of production (Rs. Per unit), the
sale price (Rs. Per unit), shipping cost (Rs. Per unit) in the cells of matrix monthly capacities and
monthly requirements are given below:
Factory
Sales agency
1
2
3
4
Monthly
capacity
(units)
Cost
of
production
A
7
5
6
4
10
10
B
3
5
4
2
15
15
C
4
6
4
5
20
16
D
8
7
6
5
15
15
Monthly
requirements
(units)
8
12
18
22
Sales price
20
22
25
18
Find the monthly production and distribution schedule which will maximize profit.
QUESTION 3
(10)
Imagine yourself to be the Executive Director of a 5-star Hotel which has four banquet halls that
can be used for all functions including weddings. The halls were all about the same size but the
facilities in each hall differed. During a heavy marriage season, 4 parties approached you to
reserve a hall for the marriage to be celebrated on the same day. These marriage parties were told
that the first choice among these 4 halls would cost Rs. 10,000 for the day. They were also
required to indicate the second, third and forth preferences and the price that they would be
willing to pay. Marriage party A and D indicated that they won’t be interested in halls 3 and 4.
Other particulars are given in the following table:
Revenue per hall
Marriage Party
I
2
3
4
A
10,000
9,000
-
-
B
8,000
10,000
8,000
5,000
C
7,000
10,000
6,000
8,000
D
10,000
8,000
-
-
Where (–) indicates that the party does not want the hall. Required: Decide on an allocation that will maximize the revenue to your hotel.
QUESTION 4 (10)
.
Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes it can be sold for $160,000. The current property owner asked for bids and stated that the property will be sold for the highest bid in excess of $100,000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100,000
and $150,000.
a.
Develop a worksheet that can be used to simulate the bids made by the two competitors. Strassel is considering a bid of $130,000 for the property. Using a simulation of 1000 trials, what is the estimate of the probability Strassel will be able to obtain the property using a bid of $130,000?
b.
How much does Strassel need to bid to be assured of obtaining the property? What is the profit associated with this bid?
QUESTION 5
(10)
Megley Cheese Company is a small manufacturer of several different cheese products. One of
the products is a cheese spread that is sold to retail outlets. Jason Megley must decide how many
cases of cheese spread to manufacture each month. The probability that the demand will be six
cases is 0.1, for 7 cases is 0.3, for 8 cases is 0.5, and for 9 cases is 0.1. The cost of every case is
$45, and the price that Jason gets for each case is $95. Unfortunately, any cases not sold by the
end of the month are of no value, due to spoilage. How many cases of cheese should Jason
manufacture each month?
QUESTION 6
(10)
(i) The following data represent 15 quarters of manufacturing capacity utilization (in percentage).
Quarter/Year
Utilization
Quarter/Year
Utilization
1/2000
82.5
1/2002
78.8
2/2000
81.3
2/2002
78.7
3/2000
81.3
3/2002
78.4
4/2000
79
4/2002
80
1/2001
76.6
1/2003
80.7
2/2001
78
2/2003
80.7
3/2001
78.4
3/2003
80.8
4/2001
78
a.
Compute three-and four – quarter moving average for this time series. Which moving average provides the better forecast for the fourth quarter of 2003?
b.
Use smoothing constant of α =0.4 to develop forecast for the fourth quarter of 2003.
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(ii) An airlines organization has one reservation clerk on duty in its local branch at any given time. The clerk handles information regarding passenger reservations and flight timings. Assume
that the number of customers arriving during any given period is Poisson distribution with an arrival rate of eight per hour and that the reservation clerk can service a customer in six minutes on an average, with an exponentially distributed service time.
(a)
What is the probability that the system is busy?
(b) What is the average time a customer spends in the system?
(c)
What is the average length of the queue and what is the average number of customers in the system?