## Quantitative Methods

Quantitative Methods

1. To provide all workings

2. APA Citation if needed
Question 1

GG Manufacturing is the distributor for medical grade freezer. Their two signature products are: Ultra Freeze and Nano Freeze, whose profits are \$9000 and \$12000, respectively. The company showroom has a maximum storage capacity of 50 cubic feet and each freezer takes up 5 cubic feet of storage. To secure the freezer, a special locking mechanism has to be attached to the freezer. Ultra Freeze requires 15 of such locking mechanism, while Nano Freeze requires 8 such locking mechanisms. In total, there are 120 locking mechanism available in the showroom. Every freezer in the showroom needs to be protected with protection panel, where each unit of Ultra Freeze needs 1 while Nano Freeze needs 2 of such panel. There are only 16 protection panels available in the showroom. The sales team also cautioned that due to the uncertain economic situation, the daily demand for each type of freezer is expected to cap at 7 units each.

(a) Based on the above scenario, develop the case as a linear programming model to determine the ideal units of freezer to be stocked up daily.
(10 marks)

(b) Apply graphical and simultaneous equation approach to solve the linear programming model. You are required to identify the feasible region, solve for each corner point and identify the optimal solution.
(18 marks)

(c) Solve for the sensitivity output using Microsoft Excel Solver.
(3 marks)

(d) Interpret the reports and discuss the following scenarios (without re-solving it using Microsoft Excel Solver):

(i) If the profit on Nano Freeze is reduced to \$6000, explain if there will be any changes to the original optimal mix and total profit?
(3 marks)

(ii) The maximum storage capacity turns out to be actually 45 cubic feet instead of 50 cubic feet. How will this affect the solution?
(6 marks)

Question 2

Since 2009, there are eight rounds of cooling measures being introduced by the Singapore Government with the objective of easing the property market. There are differing views among the property analysts on whether now is a good time to enter the market, especially homes in the Core Central Region (CCR). Homes in the Core Central Region (CCR) are commonly referred to as high-end or luxury homes. According to the Urban Redevelopment Authority (URA), the CCR comprises postal districts 9, 10, 11, Downtown Core and Sentosa.

Some analysts argue that price has already bottomed while some analysts view that the price will cool further. Table 1 shows the Property Price Index (PPI) of Non-Landed Properties in CCR (by quarter) from 2008 Q1 to 2016 Q2.
Your relative whom is keen to purchase his second property in the CCR seeks your recommendation.

Table 1: Industries in PPI Quarter Price Index Quarter Price Index
2008-Q1 131.3 2012-Q2 139.2
2008-Q2 131.2 2012-Q3 139.4
2008-Q3 127.6 2012-Q4 140.3
2008-Q4 119.4 2013-Q1 141.2
2009-Q1 100 2013-Q2 140.9
2009-Q2 94.8 2013-Q3 140.5
2009-Q3 109.2 2013-Q4 137.6
2009-Q4 117.2 2014-Q1 136.2
2010-Q1 122.4 2014-Q2 134.2
2010-Q2 128.9 2014-Q3 133.1
2010-Q3 131 2014-Q4 131.9
2010-Q4 133.9 2015-Q1 131.4
2011-Q1 135.3 2015-Q2 130.6
2011-Q2 137.5 2015-Q3 129
2011-Q3 138.5 2015-Q4 128.6
2011-Q4 139.2 2016-Q1 129
2012-Q1 138.4 2016-Q2 129.4

Refer to the data file provided. The data file contains the monthly industry sector sales performance from January 2013 to June 2016. The base year is 2009 (2009 Q1 = 100).

Source: https://data.gov.sg/dataset/price-indices-of-non-landed-properties-by-locality

(a) Use the PPI values in Table 1 to analyse and discuss your observations.
(15 marks)
(b) Develop an overall conclusion of your analysis by

i. Justifying an appropriate forecasting model for the PPI,
ii. Deriving the forecasting model and forecasting the PPI up to 2017 Q4,
iii. Discussing the potential pitfalls and stating your recommendations.
(15 marks)

Question 3

A local fashion retailer is seeking a new retail outlet in the neighbourhood estate. The property agent recommended two possible sites. One of the sites (Site A) is near to the bus interchange and is relatively small, while the other site (Site B) is further away but has a larger floor area.

If the retailer opens the store at Site A and demand is good, the store will generate an annual profit of \$200,000. If demand is low, the retailer will lose \$40,000 per annum. If the retailer opens at Site B and demand is high, the store will generate an annual profit of \$320,000, but the store will lose \$120,000 per annum if demand is low. The retailer also has the option of not opening the new retail outlet. The retailer believes that there is a 55 percent chance that demand will be high.
The retailer is offered a market research study by the property agent. The probability of a good demand given a favourable study is 0.85 while the probability of a good demand given an unfavourable study is 0.1. There is a 70 percent chance that the study will be favourable.

(a) Determine, using the decision tree approach, whether the retailer should purchase the market research study. Show the decision tree and compute the expected values for all relevant nodes.
(26 marks)

(b) Determine the maximum amount the retailer would be willing to pay for this study.
(4 marks)