You are the President of the Graduate Student Council in APU and is considering selling fruits during Entrepreneur Week 2020.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Question 1 (10 marks) 

You are the President of the Graduate Student Council in APU and is considering selling fruits during Entrepreneur Week 2020. Because some of the fruits such as strawberries are already very ripe, you will need to sell them immediately and then discard any that remain unsold. You have estimated that you will be able to sell 15, 16, 17, 18, 19 or 20 cases in one day and the probability is shown in the table below. You purchase the fruits for $7 per case and sell them for $18 per case. 

Demand	Probability
15	0.10
16	0.30
17	0.15
18	0.20
19	0.15
20	0.10

To decide how many fruit cases to purchase, you are required to construct a payoff table for this decision situation. Then use the following decision-making methods (A and B) with and without probabilities to determine the best decision.

Method (A)    Minimax regret approach

Method (B)     Decision tree analysis (Hint: you are required to compute the expected value of perfect information.) 

Comment the results if there is any discrepancy of decisions between Method A and B.

 Question 2 (10 marks) 

You will set up a booth to sell fruit case during Entrepreneur Week 2020. To properly plan for this booth, you are required to:

(a) Develop a table with at least 8 different activities to show the requisite activities, their immediate predecessors and the estimated completion time (in days) since you are only given 2 weeks to prepare. Assume this is a new event that you never be worked   before, you are required to provide the optimistic, most probable and pessimistic time estimates (in days) for each activities you are listed in the table.4 marks)

(b)        Use R to determine the activity schedule for the event in part (a) and identify the critical path. Based on the analysis, can the event in part (a) be prepared in the time given? If not, provide suggestion to ensure the booth is ready in 2 weeks.    (6 marks)

 Question 3 (15 marks) 

(a)          To successfully set up the booth to sell the fruit cases, you are required to assign the tasks you described in Question 2 to your team members so that all the activities can be done in the time given. Assuming:

·         only 10 of your team members are available and

·         each of them can handle at most 2 tasks at the same time. 

Formulate a model to determine how the tasks to be assigned to the staff so that the booth can be prepared in the days you mentioned in Question 2(b). To answer this question,      you are required to consider all possible member-activity assignments and estimate the corresponding completion times.(8 marks)

(b)  There is a Team B plans to sell fresh fruit juice during Entrepreneur Week 2020? Each of you is considering three possibilities to promote: (I) better packaging, (II) increase      advertising, and (III) slight reduction in price. Each gain in your team will result in an identical loss in Team B. The table below shows the percentage of increase or decrease of sales for your team using the three possibilities:

 Identify whether the above problem has a pure strategy solution. Then, determine the strategy both teams (including my team) should be used to promote the product.(7 marks)

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