1. This question will test your ability to understand OPL code.
2. An oil renery obtains crude oil from 3 dierent sources. The renery distills up to
100,000 barrels of crude oil per day in its fractionater. The fractionater heats up the
crude oil until various products called DN (distillation naphtha), DHO (distillation
heating oil), and DGO (distillation gas oil), are given o in vapour form and collected
at various levels. Other non-usable byproducts are also produced and discarded. It
costs $0.75 to run the fractionater on a barrel of crude oil. The table below illustrates
the outputs of the fractionater for each type of crude.
3. A company supplies toner for oce photocopiers. They have m clients C = f1; : : : ;mg
and n distribution centers D = f1; : : : ; ng. Each client i has di units of toner they
demand and must be satised by the distribution centers. Note: Multiple distribution
centers can supply any one client.
Depending on which distribution center supplies any particular client, a certain amount
of prot is incurred. The prot function for the total amount of demand x that center
j satises is a concave function profitj(x) where
0:5x if x 40
cjx 40(cj 0:5) otherwise
and cj is a specic constant for center j that is always bigger that 0.5.
The company transports the toner using delivery trucks where each truck is assigned
to a specic center. Each center has a constant G units of fuel to keep the trucks going.
The amount of fuel needed by the trucks at center j to supply x units of toner is a
convex function fuelj(x) where
0:75x if x 60
2x 75 otherwise
Give a linear program that maximizes the prot of the company.
4. For each part, determine if the given mathematical program and the given LP are
equivalent (ie. will give the same optimal value). Justify your conclusion.