National Paper runs a paper plant in Maine that buys pulp and turns it into three types of paper products: food contact paper, high-speed inkjet paper, and envelope paper. They need to plan their production schedule for the next quarter. The plant has two machines (each the size of a football field), and each machine works independently to produce the product it has been assigned. The plants run 24 hours per day, seven days a week, and so an entire quarter equals 2000 hours of useable production time (some hours during the quarter are set aside for cleaning and maintenance and are not included in this 2000 hours). Despite the plants nonstop production, recent demand for their three products has skyrocketed, and the plant cannot satisfy demand for all of their products. Quarterly forecasted demands for the three types of paper products are currently: 480000 tons of food contact paper, 280000 tons of inkjet paper, and 120000 tons of envelope paper. The two machines that make these three products are of different types and produce paper products at different rates. These rates (tons per hour) are given in the table below:

Now suppose each machine must first be set up to make each type of paper product, and this requires 48 hours of preparation, which comes out of that machines useable production time of 2000 hours. At the start of the quarter, assume neither machine is set up to make anything, and so a setup is required.

3c. Write out a new formulation in its entirety that incorporates this set up requirement. Clearly label all decision variables and their types.

Machine Food Contact Inkjet Envelope Machine 1 150 tons/hour 200 tons/hour 180 tons/hour Machine 2 135 tons/hour 200 tons/hour 170 tons/hour Margins (profit margins), measured in dollars per ton, are given in the table below. Food Contact Inkjet Envelope $1250/ton $1000/ton $1100/ton