Silva and Sons Ltd. (SSL) is the largest coconut processor in Sri Lanka. SSL buys coconuts at 300 rupees per thousand to produce two grades (fancy and granule) of desiccated (dehydrated) coconut for candy manufacture, coconut shell flour used as a plastics filler, and charcoal. Nuts are first sorted into those good enough for desiccated coconut (90%) versus those good only for their shells. Those dedicated to desiccated coconut production go to hatcheting/pairing to remove the meat and then through a drying process. Their shells pass on for use in flour and charcoal. The 10% of nuts not suitable for desiccated coconut go directly to flour and charcoal.

SSL has the capability to hatchet 300,000 nuts per month and dry 450 tons of desiccated coconut per month. Every 1000 nuts suitable for processing in this way yields 0.16 ton of desiccated coconut, 18% of which is fancy grade and the rest granulated. Shell flour is ground from coconut shells; 1000 shells yield 0.22 ton of flour. Charcoal also comes from shells; 1000 shells yield 0.50 ton of charcoal.

SSL can sell fancy desiccated coconut at 3500 rupees per ton over hatcheting and drying cost, but the market is limited to 40 tons per month. A contract requires SSL delivery of at least 30 tons of granulated-quality desiccated coconut per month at 1350 rupees per ton over hatcheting and drying, but any larger amounts can be sold at that price. The market for shell flour is limited to 50 tons per month at 450 rupees each. Unlimited amounts of charcoal can be sold at 250 rupees per ton.

max 3500s1 + 1350s2 + 450s3 + 250s4 - 300p1 - 300p2

s.t. 0.10p1 - 0.90p2 = 0

0.82 s1 - 0.18s2 = 0

p1 <= 300

s1 + s2 <= 450

s1 <= 40

s2 >= 30

s3 <= 50

0.16p1 - s1 - s2 = 0

0.11p1 + 0.11p2 - 0.50s3 - 0.22s4 = 0

p1, p2, s1, s2, s3, s4 >= 0

Question - Explain the 8th constraint and state the dual of your primal linear program.