Problems:
1. ABC wants to plan its electricity capacity for the next T years. ABC has a forecast of dt megawatts for electricity during year t = 1,... T. The existing capacity which is in the form of oil-fired plants will be et for year t (these plants will never be retired). There are two alternatives for expanding electric capacity: coal-fired or nuclear plants. There is a capital cost of ct per mega watt of coal-fired capacity that becomes operational at the beginning of year t. The corresponding cost for nuclear plant is nt. For safety reasons, it has been determined that no more than 20% of capacity should ever be nuclear. Coal plants last for 20 years, while nuclear plants last for 15 years. Formulate a linear program that will give the least cost capacity expansion plan.
2. Consider the polyhedron P = {(x1, x2, x3)T € R3 | x1 + x2 + x3 ≤ 1; x1,x2,x3 ≥ 0}
(a) Find all the extreme points.
(b) Represent the vector x = (1/3, 1/3, 1/4) T in terms of the extreme points.