A large copper company16 has 23 plants, each of which can burn 4 different kinds of fuels to produce the energy needed in smelting. Energy requirements at each plant p are known quantities rp. We also know the energy output ef of each ton of fuel f burned and the quantity of sulfur pollution sf released per ton of fuel f burned. Costs vary by location, but estimates cf, p are available of the cost per ton for fuel f at plant p. We want to choose mixes of fuels at plants to fulfill energy needs while minimizing both cost and pollution.

(a) Briefly justify why appropriate decision variables for this problem are 1f = 1,c, 4; p = 1,c, 232 xf, p ! amount of fuel f burned at plant p

(b) Write an objective function minimizing total energy cost.

(c) Write an objective function minimizing total sulfur pollution.

(d) Write a system of main constraints requiring that sufficient energy be produced at each plant. Also indicate how many constraints there are in this system.

(e) Complete your model with an appropriate system of variable-type constraints.

Also indicate how many constraints there are in this system.

(f) Is your model best classified as an LP, an NLP, an ILP, or an INLP, and is it singleor multiobjective? Explain.