solve by linear programming and cplex

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 $2,000,000 in profits from their five products. To manufacture plastic toys, Toysco purchases recycled plastic for $70/ton and new plastic for $100/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 11 tons. Table 1 shows the price of each toy and the required plastic to produce the toys. Due to quality requirements, at least 20%, 10%, 25%, 60%, and 40% 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. Report Month 1 2 3 4 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 $1/per item. In such a case, the item is placed on backorder and the order must be shipped to the customer at some future time. Demand of each product over the next 12 months is shown in Table 2. You must assume that you have nothing in inventory or items that are backordered, and that you must end at the end of the 12th month with the same condition. 67 Table 1 - Selling Price of Each Type of toy and required plastic Selling Price ($) Required plastic Toys 7 8 9 10 11 12 Truck Mini slide Toy tools Stacking rings Duck Truck Table 2-Demand of each type of toy over the next 12 months Beam Toy tools 3,000 1,000 700 1,400 2,000 2,000 1,000 1,700 2,000 3,000 1,000 700 $27 $45 $22 $15 $8 Mini slide 1,400 300 900 800 1,400 900 900 1,000 1,700 1,500 1,900 2,000 (lb) 2 10 1.5 1.5 0.5 2,700 2,400 3,100 1,600 3,600 3,700 2,000 3,100 3,300 3,000 2,000 3,100 Stacking rings 2,500 1,300 500 3,300 2,100 1,500 1,000 800 4,100 2,000 2,800 100 Duck 1,200 1,500 4,300 3,900 800 200 3,500 1,200 2,200 1,300 4,100 1,000