Show the relevant solution output and sensitivity output

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Reference no: EM131223218

Quantitative Methods Assignment -

Question 1 -

Cha Cha Pte Ltd is a home-grown company that supplies pre-mixed tea leaves to the regional hotels and restaurants. Their two best seller tea leaf blends are Fragrance026 and Scent012. Due to the upcoming festive season, there is a consolidated order commitment for at least 150 kg of Fragrance026, and 200 kg of Scent012. To produce 1 kg of Fragrance026, it should contain at most 55 percent dried figs while each kg of Scent012 should contain at least 65 percent of orange peel. The source for orange peel comes from two mixtures; mixture Alpha and mixture Beta. Mixture Alpha contains 70 percent orange peel and 20 percent dried figs, while mixture Beta contains 25 percent orange peel and 60 percent dried figs. Mixture Alpha costs 85 cents per kg and mixture Beta costs 40 cents per kg. The company CEO would like to know the cost-effective way of mixing Alpha and Beta.

(a) Develop the portfolio selection case as a linear programming problem. Please explain clearly how you choose the decision variables, formulate the objective function and constraints.

(b) Solve for the optimal solution using Microsoft Excel Solver. Show the relevant solution output and sensitivity output.

(i) If the cost of Mixture Alpha is 50 cents, explain if there will be any changes to the original optimal mix?

(ii) If the order for Fragrance026 is actually 50kg instead of 150kg, what would be the implications on the total cost on acquiring mixture Alpha and Beta?

Question 2 - Singapore's Tourist Arrival

A bridge between the East and the West for centuries, Singapore embraces tradition and modernity. Colourful ethnic precincts amongst efficient business centres, and serene gardens set against sleek skyscrapers, Singapore is a fascinating destination for leisure and business travellers (MTI, 2015).

Over the years, there has been remarkable transformation in Singapore's tourism landscape and there are various reported record growth in both tourism receipts and visitor arrivals. Since 2004, Singapore has grown her tourism receipts by almost 2.5 times while visitor arrivals also almost doubled (MTI, 2015).

A common key performance indicator is the International Visitor Arrivals which refer to travellers taking a trip to Singapore whose length of stay is less than a year. This excludes:

All Malaysian citizens arriving by land;
Returning Singapore citizens, permanent residents and pass holders
Non-resident air and sea crew (except for sea crew flying in to join a ship); and
Air transit and transfer passengers.

Arrival statistics are reported by country of residence based on information from Disembarkation/Embarkation (D/E) Cards by the Immigration and Checkpoints Authority of Singapore (STB, 2015).

Using the data in Tables 2.1, 2.2 and 2.3 below, produce forecasts of the Visitor Arrivals in Singapore (Total, ASEAN and China) and prepare a report according to the requirements listed.

Table 2.1: Total Visitor Arrivals in Singapore TOTAL VISITOR ARRIVALS (in Thousands)

Year	Quarter
Year	1	2	3	4
2011	3118	3237	3486	3329
2012	3576	3506	3648	3765
2013	3882	3851	4079	3755
2014	3881	3635	3870	3708
2015	3643

Table 2.2: Visitor Arrivals in Singapore Originating from ASEAN VISITOR ARRIVALS - From ASEAN (in Thousands)

Year	Quarter
Year	1	2	3	4
2011	1209	1394	1397	1412
2012	1341	1487	1406	1544
2013	1389	1589	1543	1644
2014	1446	1614	1484	1567
2015	1290

Table 2.3: Visitor Arrivals in Singapore Originating from China VISITOR ARRIVALS - From CHINA (in Thousands)

Year	Quarter
Year	1	2	3	4
2011	411	346	472	347
2012	542	436	537	518
2013	647	593	670	358
2014	557	314	460	390
2015	509

Source: partially extracted from Department of Statistics (2015) Statistical Tables from Economic Survey of Singapore

https://www.singstat.gov.sg/docs/default-source/default-document- library/statistics/browse_by_theme/economy/statistical_tables/essa111.xlsx (Accessed 8th July 2015)

(a) Provide an understanding and background discussion on the methodology of forecasting.

(b) Determine the seasonality of the data by conducting an in-depth seasonality analysis for Table 1, 2 and 3. For each quarter, indicate the seasonal indexes, the deseasonalised time series and the trend line that will fit the deseasonalised time series. Adjust the seasonal indexes, if necessary. Provide justification on the appropriateness of seasonality analysis.

(d) Develop an overall conclusion of your forecasting findings, policy observations and recommendations.

Question 3 -

SIMSIM Pte Ltd is a boutique fund manager and venture capitalist. It has recently took part in a Series B round of financing exercise and has been presented with four potential proposal (P1, P2, P3 and P4). The analyst has been tasked to provide some insights in decisions to be made.

Table 3.1: Payoff (in $Millions) Table

	ECONOMIC CONDITION
	Poor	Average	Good	Excellent
PROPOSAL	(S1)	(S2)	(S3)	(S4)
P1	50	75	20	30
P2	80	15	40	50
P3	-100	300	-50	10
P4	25	25	25	25
Probabilities	0.4	0.2	0.25	0.15

(a) Identify the decisions to be made if the corporate strategy is to undertake an optimistic stand or a conservative stand. Show your workings.

(b) Determine the decision to be made using the decision tree approach. Show the decision tree and compute the expected values for each node as well as determine the expected value of perfect information. Interpret the results.

References:

Ministry of Trade and Industry Singapore - Insights: Tourism 2015 goals. Website:

https://www.mti.gov.sg/MTIInsights/Pages/Investments.aspx (Accessed 8th July 2015)

Singapore Tourism Board - Statistics and Market Insights. Website:

https://www.stb.gov.sg/statistics-and-market-insights/pages/statistics-Visitor-Arrivals.aspx (Accessed 8th July 2015)

Statistical Tables from Economic Survey of Singapore, Department of Statistics. Website:

https://www.singstat.gov.sg/docs/default-source/default-document- library/statistics/browse_by_theme/economy/statistical_tables/essa111.xlsx (Accessed 8th July 2015).

Reference no: EM131223218

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len1223218

9/28/2016 3:16:02 AM

This is a group-based assignment. You should form a group of 3 members from your seminar group. Each group is required to upload a single report to MyUniSIM via your respective seminar group. Please elect a group leader. The responsibility of the group leader is to upload the report on behalf of the group. It is important for each group member to contribute substantially to the final submitted work. All group members are equally responsible for the entire submitted assignment. If you feel that the work distribution is inequitable to either yourself or your group mates, please highlight this to your instructor as soon as possible. Your instructor will then investigate and decide on any action that needs to be taken. It is not necessary for all group members to be awarded the same mark.

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