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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 will be successful. If successful, revenue of $5,000 will be realised. If you decided to launch this Product and itis unsuccessful, a loss of $3,000 will occur.  

Before making the decision, you are considering to ask Serenato conduct a market surveyThe 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 is success is 0.85. If the surveyis negative, the probability that this Product 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

(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 20 days 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 or Microsoft Project to determine the activity schedule for the event in (a) and identify the critical path. Based on the analysiscan 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: 

 

• only 8 of your friends are available
• each of them can handle at most 3 tasks at the same time

 

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,  

 

(a) formulate a transition matrix for the above problem. 

(7 marks)

(b) use R to solve the matrix in part (a) and interpret the results.  

(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: 

 

Time

Number of Staff

9am – 10am

5

10am – 11am 

5

11am – 12pm

5

12pm – 1pm

9

1pm – 2pm

9

2pm – 3pm

7

3pm – 4pm

5

4pm – 5pm

5

 

The proposed working schedule is as below: 

• Three of your friends will come to help. 
Two of them come at 10am and works for 3 hours. 
Another comes at 12pm and works for 4 hours. 
• Helpers are required to work for 3-hour shift beginning on the hour. 
(a) Assuming each helper is paid $10 each hour, you are required to determine how many helpers required so that the cost can be mininised. Based on your output, develop a schedule to show the allocation of the helpers. 

(7 marks)

(b) Your friend, Meena also suggested that the helpers can be assigned either a 3-hour or a 4-hour shift so that the number of helpers can be reduced to 15. Revise the model in (a) by considering both 3-hour and 4-hour shift and determine whether Meena’s suggestion is correct. 

(8 marks)

Question 6 (15 marks)

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

(a) Construct a network to show at least 10 various areas/cities/landmarks/buildings that might pass from the company to APU

(4 marks)

(b) Of all possible routes available at the areas/cities/landmarks/buildings you mentioned in part (a) to APU, determine the shortest time (in minutes) using

(i)Linear programing or Dijkstra shortest path algorithm.

(4 marks)

(ii)Prims, Kruskal or Boruvka algorithm. 

(4 marks)  

(c) Comment on your results in part (b). 

(3 marks)

 

 

Task B (25 marks)

 

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

(a) Based on data you collectperform the following analysis:
(i) Estimate the arrival and service rate. 

(2 marks)

(ii) Compute the operating characteristics of the waiting line model by assuming Poisson arrivals and Exponential service times. 

(5 marks)

(b) To evaluate the performance of the waiting line system in (a), you are required to run simulation with 80customers using Excel. Construct
(i) bar chart to show the waiting and service time of customers 

(2 marks)

(ii) histogram of waiting time 

(2 marks)

(iii) histogram of service time 

(2 marks)

(c) Based on your result in (b)perform the following
(i) Find the average waiting time. 
(ii) Find the probability that a customer has to wait. 
(iii) Find the average service time.
(iiii) Find the average time a customer spends in the system. 

(4 marks)

 

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

Programming Database Programming Data Analysis Data Mining Data Integration Matematika Matematic

Published Budget: Rp 500,000
Finish Days: 2
Published Date: 31/07/2019 09:19:57 WIB
Start Date: 01/08/2019 05:45:42 WIB
Finish Date:
Project Status: Closed
Accepted Worker: JanuarWR (JanuarWR)
Accepted Budget: Rp 400,000
Project Ending: Self Mediation

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