Sample Paper

GMBA DXB; Apr 2010

END TERM EXAM QT-2

Time: 100 mins

Full marks = 100 (5 questions, each of 20 marks)

All questions are compulsory

Rules:

1) This booklet is the question paper-cum-answer paper.

2) Answer in this booklet ONLY and submit THE ENTIRE BOOKLET (stapled, as it is)

3) DO NOT TEAR THE PAGES OF THIS BOOKLET, ELSE ANSWER SHEET WIL NOT BE ACCEPTED.

4) DO NOT DO ANY ROUGH WORK ON THIS BOOKLET. Ask for SEPARATE SHEETS AND SUBMIT THEM

5) SAVE YOUR FILES IN SEPARATE EXCEL SHEETS (PREFERABLY WITH A SOLVER MACRO IN EACH)

6) STAY CALM, WORK NEATLY, YOU WILL DO WELL.

7) If your Solver jumps around, from tree to tree, run it a few more times and put your most appropriate answer along with all the other 4 or 5 answers. Circle your MOST PREFERRED Ans & also put it inside the Answer Box

8) Write final answers ONLY inside the designated boxes that are provided with almost all questions

9) WRONG DATA ENRY WILL INVITE ZERO MARKS, no matter how correctly the problem is done

Question 1

Water is being distributed by a private carrier from 3 wells (Pull, Tull & Mull) and supplied to 4 villages (Ching, Ming, Ping & Ding). The daily supply & demand for water, in number of truck-fills possible to be supplied from each well, and the minimum demand, per village, are given below. The cost per truck from each well to each village is also given below. Find the optimum allocation plan and the outcome of such a plan.

		Unit cost of transportation per truck-fill (in $)
		Villages				Max Supply
		Ching	Ming	Ping	Ding
	Pull	30	24	21	32	160
Wells	Tull	27	15	19	27	145
	Mull	17	19	20	26	45
	Max Demand	65	100	130	55
DO NOT DO YOUR ROUGH WORK ON THIS PAGE. USE SEPARATE SHEETS FOR THAT
a) Write ONLY your FINAL Optimal allocation inside the GRID and also the OFV in the BOX below
	FINAL Allocation
	Ching	Ming	Ping	Ding
Pull
Tull
Mull
				Answer =			(in $)

b) Of all the unused connections, which one has the most acceptable reduced cost, and hence the potential to use them, in case a bottleneck arises on any existing used connection
				Answer =

Question 2

A producer of kitchen equipments wants to maximize his earnings from manufacture and sale of chopping boards (CB) and knife holders (KH). CB gives a profit of $10 per unit while KH $22 per unit. The technical requirements of the four resources and their available stock appear in the table below. Only completed items are sold, and there is a conscious desire to avoid going for uncompleted or semi-finished equipment’s in inventory; and the producer obviously knows how to manage this. Also, a fixed cost of $17 and $15 are incurred for CB and KH respectively even if a single piece of that item is made. Find the optimal solution.A61:H81

for CB

for KH

Stock

Unit

Cutting

14

8

140

mins

Gluing

5

13

100

mins

Finishing

3

8

70

mins

Packing

4

2

56

mins

DO NOT DO YOUR ROUGH WORK ON THIS PAGE. USE SEPARATE SHEETS FOR THAT

a) Write all equations neatly using notations 'CB' & 'KH' for the two brands & other relevant variables

b) Write all your final answers ONLY inside the 4 set of boxes provided below.

CB =

Name the binding

constraint(s) if any

HK =

OFV =

Question 3

In a bid to diversify portfolio, the following 5 scrips appear important for three investors T, L and E who had varying degrees of risk appetite. Each investor expressed a minimum return for his respective portfolio: Investor T wanted 9.6, investor L wanted 10.5 & investor E wanted 11.8 as their minimum. Eventually, this minimum value of return was exactly honored and paid to them by their investment banker. Answer the following questions below. Assume there is no correlation between the movements of these 5 scrips

			all figures are in % form, hence ignore % from all your calculations
		cement	natural gas		steel	pharma		auto
avg return ($)		9.7	18.2		8.6	12.4		11.6	(per share of $100)
stdev of return		11	14		7	15		13
Answer the two sets of questions, given at the top of the boxes below.
DO NOT DO YOUR ROUGH WORK ON THIS PAGE. USE SEPARATE SHEETS FOR THAT
a) For each investor, state the vector of matrix product, given by the expression [DV] x [COV]
MAX 2 Places of Decimals
		CAUTION: DO NOT GIVE THE D.V.'s IN THE BOXES BELOW.
		[DV] x [COV]
Investor		cement	natural gas		steel	pharma		auto
T
L
E
b) Fill up the boxes below, whichever is/are applicable
								MAX 2 Places of Decimals, if reqd
Investor	Pooled Variance			Indicate which investor(s) got cheated, & why?			If cheated, how much money he lost (in $) over his total portfolio ++
T
L
E

++ Assume each investor spends $360,000 in his above portfolio (each share, has face value = $100)

Question 4

Flower vendor Manaswini sells flowers at $12 a piece. She buys them for $7 a piece from wholesale dealer, Shamik. Orders for next day are given the previous evening. Unsold flowers at end of day, are taken by Shamik for a refund of $3 per flower. The pattern of flower sale, faced by Manaswini in the past, is given below:

No of flowers per day	20	21	22	23	24	Total
Days of sale	45	65	75	80	35	300
DO NOT DO YOUR ROUGH WORK ON THIS PAGE. USE SEPARATE SHEETS FOR THAT
a) Fill up the Conditional Profit table below
	Manaswini's Decisions
Demand for Flowers	20	21	22	23	24
20
21
22
23
24
b) What is the optimum stocking plan that you can suggest to Manaswini, and why?
		why? =			stock =
c) Consultant Praveen comes into the scene and promises to consistently provide her with perfect information, about market demand expected the next day. Incidentally, whatever Praveen says, comes true. What is the charge Manaswini is likely to pay to Praveen, for such accurate demand forecasting services?
				USE upto MAX 2 Places of Decimal, if required
			Consultant's Fees

Question 5

A manager has to decide how many machines of a certain type she has to buy. She has two options, either buy one machine, or buy two machines. If she buys one machine and market demand is more than the company can handle, then a second machine can be procured at a later date. But it might be a more expensive proposition. Hence, the cost of buying two machines now, will be more economical. She has to take a call. Now, if the initial purchase is straightaway for two machines and market demand is high, she gets a net return of $140,000. But if market demand is low, she then gets $75,000. [The chance of low (high) market demand emerging is 0.45 (0.55), which obviously, she has no control over]. However, if her initial purchase is for one machine, she gets a net return of $85,000 whenever associated demand is low. But, if market demand turns out to be high, she has three options to go for. One, she does nothing and keeps getting the same net return she was getting with one machine & low demand. Two, she buys a second machine which gives her $115,000 net return. Three, she sub-contracts. In which case, she is exposed either to Mr. Yuvraj Singh with a probability of 0.65 & getting a net return of $130,000, or to Mr. Rohit Sharma with a net return of $155,000 on a chance of 0.35. She cannot opt for any one of them, since this is done by the head of the sub-contracting union. How many machines should the manager buy? What is the economic value of this best option she gets?

DO NOT DO YOUR ROUGH WORK ON THIS PAGE. USE SEPARATE SHEETS FOR THAT
a) Make a neat and complete decision tree, with all assessments at each junction
USE upto MAX 2 Places of Decimal, if required

Best Option

Value of best decision