Hawaii Sugar Company makes brown sugar, powdered sugar, processed (white) sugar and molasses from sugar cane syrup. Company buys 4000 tons of syrup weekly and is contracted to deliver at least twenty five tons weekly of each kind of sugar. Production process begins by producing brown sugar and molasses from syrup. A ton of syrup makes 0.3 ton of brown sugar and 0.1 ton of molasses. Next, white sugar is made by processing brown sugar. It takes 1 ton of brown sugar to make 0.8 ton of white sugar. At last, powdered sugar is made from white sugar through special grinding process which contains the 95% conversion efficiency (1 ton of white sugar makes 0.95 ton of powdered sugar). Profits per ton for white sugar, brown sugar, powdered sugar, and molasses are $150, $200, $230, and $35, respectively.
Formulate problem as the linear program, and find weekly production schedule.
Comment on economic feasibility of expanding processing capacity of company to more than 4000 tons of syrup weekly.
If company could selectively "buy out" its contract commitments and suppose it can still sell all product it selects to make, that contracts must it eliminate and how much more profit will yield?