Question: A paper recycling company converts newspaper, office paper, and cardboard collected from office buildings in New York city into pulp for print paper, wrapping paper, and disposable towels. The following table summarizes the yield for each kind of pulp recovered from each ton of recycled material.

For instance, a ton of newspaper can be recycled using a technique that yields 0.80 tons of wrapping paper. Alternatively, a ton of newspaper can be recycled into 0.60 tons of disposable towels. Similarly, a ton of cardboard can be recycled to yield 0.75 tons of print paper or 0.90 tons of wrapping paper. Note that newspaper cannot be converted to print paper and cardboard cannot be converted to disposable towels.

The cost of processing each ton of recycle material into the three types of pulp is shown in the following table along with the amount of each of the three recycle materials that can be purchased and their cost.

The recycling company wants to determine the least cost way of producing 900 tons of print paper, 330 tons of wrapping paper, and 500 tons of disposable towels.

Part a) List the linear program you set up for this problem.
Part b) What is the least total cost?
Part c) Explain how you will recycle to get the required 500 tons of disposable towels.
Part d) How many tons of newspaper will be used for the recycle process?
Part e) How many tons of recycle material are lost during the entire recycle conversion process?
Part f) What is the average recycle yield percentage for this recycle problem?