How to translate OPL to mathematics program
An oil re nery obtains crude oil from 3 di erent sources. The re nery 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 satis ed 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 pro t is incurred. The pro t function for the total amount of demand x that center
j satis es is a concave function profitj(x) where
profitj(x) =
0:5x if x 40
cjx 40(cj 0:5) otherwise
and cj is a speci c 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 speci c 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
fuelj(x) =
0:75x if x 60
2x 75 otherwise
Give a linear program that maximizes the pro t 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.