The Green Supply Company manufactures plastic grocery bags and milk jugs. The company can obtain 5,000 lbs of used plastic bags, 18,000 lbs of used plastic milk jugs, and 40,000 lbs of indus- trial plastic scraps (not post-consumer material) per week at costs of $18, $12, and $10 per 100 lbs respectively. The company has orders for 4,000 boxes of plastic bags and 80,000 milk jugs per week. One box of plastic bags requires 6 lbs of plastic, costs $5 to manufacture, and sells for $14. It costs $9 and requires 14 lbs of plastic to make 100 milk jugs, and the jugs retail for $20. The plastic bags must be at least 25% post-consumer recycled plastic (used bags or jugs) because of consumer preference, and the milk jugs must be at most 50% post-consumer recycled plastic for strength. Here, we are assuming that non post-consumer recycled plastic comes from the industrial scraps. Part 1: The optimal mix 1. Develop a model to determine the optimal mix of plastics for each product. Outine your model using the 5 step modelling approach Part 2: Adding an additional supplier 1. A new supplier can provide industrial plastic scraps at $8 per 100 lbs. Extend the model developed in part 1 to account for this new addition 2. Determine the new optimal mix of plastics for each product. Describe how your results differ from what you found in part 1 Part 3: The new customer 1. A new customer has offered to purchase 40,000 environmentally friendly milk jugs per week for $30 per 100 jugs. The jugs must contain at least 35% post-consumer recycled plastic. How does this change your results? 2. Should the company accept this new customer? Explain your reasoning Part 4: Relaxing a constraint Think about how your results might change f the constraint for the amount of post-consumer material required for plastic bags is relaxed. In particular, assume that this value can vary (say between 20 and 30 %) The Green Supply Company manufactures plastic grocery bags and milk jugs. The company can obtain 5,000 lbs of used plastic bags, 18,000 lbs of used plastic milk jugs, and 40,000 lbs of indus- trial plastic scraps (not post-consumer material) per week at costs of $18, $12, and $10 per 100 lbs respectively. The company has orders for 4,000 boxes of plastic bags and 80,000 milk jugs per week. One box of plastic bags requires 6 lbs of plastic, costs $5 to manufacture, and sells for $14. It costs $9 and requires 14 lbs of plastic to make 100 milk jugs, and the jugs retail for $20. The plastic bags must be at least 25% post-consumer recycled plastic (used bags or jugs) because of consumer preference, and the milk jugs must be at most 50% post-consumer recycled plastic for strength. Here, we are assuming that non post-consumer recycled plastic comes from the industrial scraps. Part 1: The optimal mix 1. Develop a model to determine the optimal mix of plastics for each product. Outine your model using the 5 step modelling approach Part 2: Adding an additional supplier 1. A new supplier can provide industrial plastic scraps at $8 per 100 lbs. Extend the model developed in part 1 to account for this new addition 2. Determine the new optimal mix of plastics for each product. Describe how your results differ from what you found in part 1 Part 3: The new customer 1. A new customer has offered to purchase 40,000 environmentally friendly milk jugs per week for $30 per 100 jugs. The jugs must contain at least 35% post-consumer recycled plastic. How does this change your results? 2. Should the company accept this new customer? Explain your reasoning Part 4: Relaxing a constraint Think about how your results might change f the constraint for the amount of post-consumer material required for plastic bags is relaxed. In particular, assume that this value can vary (say between 20 and 30 %)
