Project This project can be completed individually or in groups of 2 students. You should solve your project using the IBM ILOG CPLEX Optimization Studio. Project Description You have recently been hired as an operations research analyst in a consulting firm. Congratulations! The company now assigned you to work for Toysco, which manufactures plastic toys. You are required to help Toysco develop an optimized work schedule for the plant over the next 12 months. Last year, under a similar demand and without any optimization tools, the company cleared around $1,500,000 in profits from their five products. To manufacture plastic toys, Toysco purchases recycled plastic for $70/ton and new plastic for $90/ton. Due to the quality of the plastic, only 80% of the recycled plastic can be used to produce the products. Furthermore, due to environmental regulations, at most 4 tons of new plastic material can be purchased at any month, and the availability of recycled plastic is at most 9 tons. Table 1 shows the price of each toy and the required plastic to produce the toys. Due to quality requirements, at least 20%, 15%, 20%, 50%, and 30% of Trucks, Mini slides, Toy tools, Stacking rings, and Ducks respectively, must be manufactured from new plastic. Also, due to manufacturing limitations, Toy tools and Ducks cannot be produced at the same month. Table 1 Selling Price of Each Type of toy and required plastic

Toys	Selling Price ($)	Required plastic (lb)
Truck	$28	2
Mini slide	$45	10
Toy tools	$22	1.5
Stacking rings	$15	1.5
Duck	$9	0.5

Each product held over in inventory from one month to the next month costs the company $0.5. If demand at each month is not met, then there is a penalty cost of $1.1/per item. In such a case, the item is placed on backorder and the order must be shipped to the customer at some future time. Demand of each product over the next 12 months is shown in Table 2. You must assume that you have nothing in inventory or items that are backordered, and that you must end at the end of the 12^th month with the same condition. Table 2 Demand of each type of toy over the next 12 months

Month	Beam
Truck	Mini slide	Toy tools	Stacking rings	Duck
1	2400	1120	2160	2000	960
2	800	240	1920	1040	1200
3	560	720	2480	400	3440
4	1120	640	1280	2640	3120
5	1600	1120	2880	1680	640
6	1600	720	2960	1200	160
7	800	720	1600	800	2800
8	1360	800	2480	640	960
9	1600	1360	2640	3280	1760
10	2400	1200	2400	1600	1040
11	800	1520	1600	2240	3280
12	560	1600	2480	80	800

Report As a standard policy for your consulting firm, you need to prepare a report to Toysco. Standard format and appropriate grammar are expected. The format of the report is a one-page executive summary and a technical report (no page limit). The executive summary is intended for the CEO of Toysco. and is designed to convince him/her that your solution is better than the status quo. That is, the executive summary should include all information you feel is pertinent to your answer and should be written so that an educated (not necessarily technical) person can read, understand, and be convinced to follow your advice. The executive summary should contain proper statement of the problem, main details of the analysis, results, and recommendation(s). The technical report is intended to someone from either your company or Toysco who has expertise in industrial engineering and operations research. This person will read the technical report to validate your methodologies and verify the correctness of your decisions. You may want to include the reasons and justification of your decisions. The technical report should include an introduction, description or statement of the problem, assumptions, mathematical model, computer implementation, results, analysis and interpretation of results, recommendation(s), and conclusion. These documents must be well-written and formatted professionally. Grading 25 points to the executive summary, 55 points to the technical report, and 120 points to the correctness of your solution.