Hawaii Sugar Company produces brown sugar, processed (white) sugar, powdered sugar, and molasses from sugar cane syrup. The company purchases 4000 tons of syrup weekly and is contracted to deliver at least 25 tons weekly of each type of sugar. The production process starts by manufacturing brown sugar and molasses from the syrup. A ton of syrup produces 0.3 ton of brown sugar and 0.1 ton of molasses. Next, white sugar is produced by processing brown sugar. It takes 1 ton of brown sugar to produce 0.8 ton of white sugar. Finally, powdered sugar is produced from white sugar through a special grinding process that has a 95% conversion efficiency (1 ton of white sugar produces 0.95 ton of powdered sugar). The profits per ton for brown sugar, white sugar, powdered sugar, and molasses are $150, $200, $230, and $35, respectively.
Formulate the problem as a linear program, and determine the weekly production schedule.
If the company could selectively “buy out” its contract commitments and assuming it can still sell all the product it chooses to make, which contracts should it eliminate and how much more profit will result?