Membantu menjawab soal Matematika dengan R programing

Halo worker, saya mempunyai soal matematika dan R programming

Ketentuannya

Buat jawabannya dalam microsoft word

Dan buat kode programnya dalam R

Berikut adalah soalny

Question 1 (10 marks)

You and your friends are considering to market a Product A. Your friend, Eric stated that it has 0.7 probability that thisProduct A will be successful. If successful, revenue of $5,000 will be realised. If you decided to launch this Product A and itis unsuccessful, a loss of $3,000 will occur.  

Before making the decision, you are considering to ask Serenato conduct a market survey. The survey cost is $250. The survey will be positive or negative, indicating either a good or poor response from the students in APU. Past experience suggested that the probability of positive is 0.7. Your initial probabilities will be then revised based on whether the surveyis positive or negative. If the survey is positive, the probability that this Product A is success is 0.85. If the surveyis negative, the probability that this Product A is unsuccessful is 0.55. 

Use R to construct a decision tree and identify the best decision for your plan.

Question 2 (10 marks)  

In conjunction with Merdeka Fiesta in APU, you are proposing to set up a booth to sell the Product A as described in Question 1. To properly plan for the booth, you are required to: 

(4 marks)

(b)​Use R or Microsoft Project to determine the activity schedule for the event in (a) and ​identify the critical path. Based on the analysis, can the event in part (a) be prepared ​within 20 days? Justify your answers. 

(6 marks)

Question 3 (10 marks)  

To successfully set up the booth, you are required to assign the tasks to your friends so that the activities you mentioned in Question 2 can be done within the time given. Assuming: 

Formulate a model to determine how the tasks to be assigned to your friends so that the number of days to complete all the tasks can be minimised. To answer this question, you are required to consider all possible member-activity assignments and estimate the corresponding completion times. 

Question 4 (15 marks)  

Suppose the following figure is the floor plan on the Merdeka Fiesta and your booth is placed in Area 3. Each time, a customer chooses at random one of the doors he/she is in and moves to another area. Set up the process as a Markov and assuming Area 3 and 5 are the absorbing states,  

(7 marks)

(8 marks)

Question 5 (15 marks)  

You are required to schedule helpers so that you have sufficient helpers and with the lowest cost on the Merdeka Fiesta. The event starts from 9am to 5pm and the minimum number of helpers required in each hour is as below: 

The proposed working schedule is as below: 

(7 marks)

(8 marks)

Question 6 (15 marks)

You have contacted Company ABC in Pavilion Kuala Lumpur to provide materials required on the Merdeka Fiesta. You have requested the company to send all the materials to APU in the shortest time (in minutes). 

(4 marks)

(i)​Linear programing or Dijkstra shortest path algorithm.

(4 marks)

(ii)​Prims, Kruskal or Boruvka algorithm. 

(4 marks)  

(3 marks)

Task B (25 marks)

You are required to study a one-server waiting line systemand observe for at least 2 hours. During your observation, you have to record the customer arrival time, time the service begins and time the service ends. 

(2 marks)

(5 marks)

(2 marks)

(2 marks)

(2 marks)

(4 marks)

In your report, please include the original data, probability distribution for arrival and service time, and simulation results.