7. 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 .3 ton of brown sugar and .1 ton of molasses. White sugar is produced by processing brown sugar. It takes 1 ton of brown sugar to produce .8 ton of white sugar. Powdered sugar is produced from white sugar through a special grinding process that has a 95% conversion efficiency (1 ton of white sugar produces .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.

8. Shale Oil refinery blends two petroleum stocks,A and B, to produce two high-octane gasoline products, I and II. Stocks A and B are produced at the maximum rates of 450 and 700 bbUhour, respectively. The corresponding octane numbers are 98 and 89, and the vapor pressures are 10 and 8 Ib/in2. Gasoline I and gasoline II must have octane numbers of at least 91 and 93, respectively. The vapor pressure associated with both products should not exceed 12 Ib/in2. The profits per bbl of I and II are $7 and $10, respectively. Determine the optimum production rate for I and II and their blend ratios from stocks A and B. (Hint: Vapor pressure, like the octane number, is the weighted average of the vapor pressures of the blended stocks.)