BUS107: Represents a set of Constraints and the Feasible Solution Space (feasible region) for a given Linear Programming Model: Quantitative Methods Assignment, SUSS, Singapore

Question 1
Figure 1-1 represents a set of constraints and the feasible solution space (feasible region) for a given Linear Programming model:

(a) Solve by mathematically stating all the constraints that give rise to the feasible region indicated in the graph  Figure 1-1.

(b) Let the objective function be 𝑧 = 𝑐1𝑥1 + 𝑐2𝑥2 where 𝑐1 and 𝑐2 are positive constants. Discuss and solve the possible optimal solutions for 𝑥1 and 𝑥2 by using the graphical solution approach.

Question 2

The public works department is analyzing the flow of drainage water from the northernmost part of a newly developed city, Town 1, to the southernmost part of the city Town 6. The following Table 2-1 shows the flow capacities of the underground drainage pipe in cubic meters per second (cms). The chief planner would like to know the peak flow of drainage water from Town 1 to Town 6 that the drainage system can handle

(a) Draw an appropriate network model using the information in Table 2-1 and propose the solution to address the chief planner’s query.

(b) Now suppose that the values in Table 2-1 represent the distance between the towns, in kilometers. Propose a relevant network model that will result in the least amount of drainage piping costs possible to be paid by the public works department to connect all the towns.

Question 3
PrimeSnack is a local company that manufactures rice-based snacks for the ASEAN market. Though the majority of their products are produced in-house, some product lines are outsourced to a third-party producer. The company is always on the lookout for a  new line of snacks to produce. The food research department has created a new family of snack that uses potatoes as the base. The production manager has been tasked to make a recommendation on how this new line of snack is to be produced:

Option 1: use the existing manufacturing line and reduce the output for the current line of snacks.

Option 2: add an additional production line by using the unused space in the plant.

Option 3: outsource to a third-party producer.

Table 3-1 shows the possible annual profit for each option under different market reactions to the product: favourable, neutral, unfavourable.

(a) Appraise, by using the most appropriate method, the decision alternatives for PrimeSnack knowing that the management is neither optimistic nor conservative in their decision-making process. Show your complete workings.

(b) Based on experience, the company is aware that for any new snack product, the market reaction can be estimated with the following probability:
C1: 0.30
C2: 0.50
C3: 0.20

(i) With the probability information provided, examine which decision should PrimeSnack choose, knowing that the company seeks to maximise the value for every decision they make.

(ii) However, the company could also opt to engage a consumer research agency to perform market sensing prior to any further action. The agency’s report has proven to be very accurate. It will cost $10,000 to engage their service. How would you advise the PrimeSnack management?

Question 4
Table 4-1 represents the sales of laptop for a local electronic store

(a) Compute the forecasted laptop sales for August to December by using a simple exponential smoothing with =0.35 and =0.45. Assume the forecast for July is 250 laptop units and show your answer (round to 2 decimal places) in a table form.

(b) Examine the forecasted values that you have computed in (a) and discuss which value of smoothing constant, , is recommended. Show your workings.

(c) Global warming is a serious threat to mankind, and it has given rise to the increasing number of non-governmental organizations (NGOs) with the aim of fighting climate change. Demonstrate how the NGOs could use data and forecasting techniques in their quest to fight climate change and campaign effort.