Question: Shale Oil (20 points)

Shale Oil, located on the island of Aruba, has a capacity of 600,000 barrels of crude oil per day. The final products from the refinery include two types of unleaded gasoline; regular and premium. The refining process encompasses four stages:

i. The pure crude flows through a distillation tower that produces a feedstock

ii. The feedstock output breaks up into two paths; the first path involves feedstock flowing into a cracker unit that refines the mixture into a gasoline stock. The second path has a portion of the feedstock flowing into the blender unit.

iii. The gasoline stock (from the cracker unit) feeds into the blender.

iv. The blender unit produces the final product, regular or premium gasoline. Both the regular and premium gasoline can be produced from either the feedstock or the gasoline stock during the blending process, although at different production costs. The company estimates that the net profit per barrel of regular gasoline is $5.20 from feedstock and $7.70 from gasoline stock. The corresponding profit values for the premium are $10.40 from the feedstock and $12.30 from the gasoline stock. According to design specifications, it takes five barrels of crude oil to produce one barrel of feedstock. The cracker units cannot use more than 40,000 barrels of feedstock per day. All remaining feedstock is used directly in the blender unit to produce the end product gasoline. The demand limits for regular and premium gasoline are 80,000 and 50,000 barrels per day.

a. Using Linear Programming, determine the optimum production schedule for the refinery. Allow for the solution variables to be in fractions (non integer)

b. Suppose the capacity of the distillation tower can be increased to 650,000 barrels per day at cost of $40,000. Is it worth making this investment. (answer this question using sensitivity analysis, stating shadow price, net profit or net loss and rationale. Extract all information from the lindo output used in part a).