You may work with at most two other students in the class. You must include the names of the students you worked with at the beginning of your report. Your homework must be submitted to Canvas as a Zip file (extension .zip, no other extension allowed NO .tar, NO .7z) with the title and must consist of the following:
- A report in Word answering the questions (but without the code).
- Source files in Excel Solver or AMPLas well as the original CSV data files.
- Please also include your name in all the files you submit, either in the titles, at the top of the Word document or as comment in the software files.

Problem 1 (Linear Optimization)
Analytics EdgeRadiation Therapy starting p.433, all questions (NOTE: in Figure 22.3, Voxel 4 should be a tumor voxel (should have a white background) and Voxel 6 should be a healthy tissue voxel (light blue background).

Problem 2 (Integer Optimization)
Analytics EdgeGerrymandering New Mexico starting p.441, all questions.

Project

This project uses the same data file as Project 1.The file emis7357sp18project1.csv contains historical ticket sales and donation data for 30,019 patrons or donors to a festival for over ten years, up to 2015. You must use R for the analytics. As before, the overarching goal of the project is to help the festival organizers understand what sort of insights, if any, they can gain from using analytics in a nonprofit setting for their patron base (donors and ticketholders). For this part of the project, we focus on creating trees and clusters.We will focus on 2010-2015 data. (Subset the data set accordingly. Only keep patrons who have had some interaction with the festival during those years.)

The festival organizers would like to understand the following:

1. Donation patterns over time
a. Create a tree to predict the donations in 2015 using data from the previous 5 years (remove the donors who didn't donate during that time period)
i. Split your 2015 data between a training and a testing set. Justify the parameters of your tree and include the plot of the tree in your output. Describe your tree.
ii. Evaluate the performance of your tree on your testing set by computing the R^2.
b. Cluster the donors according to their patterns of donation over the last 5 years using hierarchical clustering. (Again, remove the donors who didn't donate during that time period)
i. Justify your number of clusters and provide a description of each cluster suitable for a manager.
ii. Plot the donation pattern over time for each cluster.
c. Cluster the donors according to their patterns of donation over the last 5 years using k-means clustering.
i. Justify your number of clusters and provide a description of each cluster suitable for a manager.
ii. Plot the donation pattern over time for each cluster.
d. Which clustering scheme do you recommend and why?

2. Ticket sales patterns over time
a. Create a tree to predict the ticket sales in 2015 using data from the previous 5 years among ticket holders who have purchased tickets during that time period.
i. Split your 2015 data between a training and a testing set. Justify the parameters of your tree and include the plot of the tree in your output. Describe your tree.
ii. Evaluate the performance of your tree on your testing set by computing its R^2.
b. Cluster the ticketholders according to their patterns of ticket purchases over the last 5 years using hierarchical clustering.
i. Justify your number of clusters and provide a description of each cluster suitable for a manager.
ii. Plot the donation pattern over time for each cluster.
c. Cluster the ticketholders according to their patterns of ticket purchases over the last 5 years using k-means clustering.
i. Justify your number of clustersand provide a description of each cluster suitable for a manager.
ii. Plot the donation pattern over time for each cluster.
d. Which clustering scheme do you recommend and why?

3. Joint analysisof donations and ticket sales
a. Create a tree to predict the amount of money a patron will spend on the festival (either through donations or ticket sales) in 2015 using data from the previous 5 years among patrons who have some activity during that time period.
i. Split your 2015 data between a training and a testing set. Justify the parameters of your tree and include the plot of the tree in your output. Describe your tree.
ii. Evaluate the performance of your tree on your testing set by computing its R^2.
b. Cluster the patrons according to their patterns of total spend on festival (donations + ticket purchases) over the last 5 years using hierarchical clustering.
i. Justify your number of clusters and provide a description of each cluster suitable for a manager.
ii. Plot the donation pattern over time for each cluster.
c. Cluster the patrons according to their patterns of total spend on festival (donations + ticket purchases) over the last 5 years using k-means clustering.
i. Justify your number of clustersand provide a description of each cluster suitable for a manager.
ii. Plot the donation pattern over time for each cluster.
d. Which clustering scheme do you recommend and why?

Report quality:

The report must be suitable to be shared with (and understood by) a company. The report must look professional, which includes:
- a cover page with SMU logo, project title, names of students,
- all pages numbered after cover page
- executive summary
- table of contents
- list of figures
- list of tables
- each question addressed in its specific section, and the answers must be well-written
- conclusions
- any source file should be included separately in the zip file. Do not copy and paste code in the main body of your report.

Attachment:- EMIS_Assignment.zip