1 Project overview For the final project, you will formulate, analyze, and solve an optimization problem sing the tools you have learned in class. You will work in a group to develop a strategy, explore a provided dataset, develop and analyze your problem formulations, and write a report describing your approach and what you have learned. 2 Forming groups You may work in groups of up to 4 students. Please email me the names of the students in your group before 9pm on Sunday, October 25, or email me to ask for help finding a group (in which case your group assignment will be provided on October 27). 3 Optimization task Your task is to assign a workers to projects, while accounting for the preferences and constraints of the workers and projects. Workers have preferences concerning which projects they would like to work on, represented as a number between -5 and 5, with -5 indicating a strong pref￾erence to not work on a particular project, and 5 indicating a strong preference to work on it. Workers also have preferences about who they work with, speci- fied as a list of people they would like to work with and another list of people they would not like to work with. Finally, each worker has a number of skills, represented as numbers between 0 and 10, with 0 indicating a total absence of the skill and 10 indicating high proficiency. Each project has different requirements in terms of the minimum or maxi￾mum numbers of workers and their required skills. An assignment of workers to projects is feasible if the requirements of each project are met and each worker is assigned to some project. However, you should come up with an objective on your own (this is an open-ended optimiza￾tion problem), and you may add other constraints if you wish. 1 4 Deliverables Produce a report that includes the following: 1. A precise formulation of at least one optimization problem related to this task, along with an interpretation of the problem, and a justification for why you think it is a good problem formulation for this optimization task. 2. A precise formulation of the dual of your optimization problem (or at least one of your optimization problems, if you formulate more than one), along with a complete interpretation of the dual (its variables, contraints, etc.). 3. An optimal solution to your optimization problem, along with a certificate of optimality from the dual problem 4. Suggestions for what could be changed about the current state of affairs in order to make an even better solution feasible (e.g., training certain workers, team-building excercises involving specific workers, etc.) The report should be written in English, structured as a paper of several pages, with complete sentences organized into paragraphs, etc. It should be submitted along with all Python code used to produce the report. Finally, each individual member of your group must separately write a paragraph or two describing their own contributions to the project, as well as the contributions of the other group members. These reports will be submitted separately. Due date: 10pm Tuesday, December 15 (probably via Gradescope, but I will announce the submission method later)