Consider the subproblems generated by the decomposition approach. Formulate the subproblem corresponding to buying a 20-year U.S. Government security at the beginning of the first period of a model consisting of 3 one-year periods. The generic decision variables to use are as follows:

b₁, S₂₁(e₂), h₂₁(e₂), S₃₁(e₃), h₃₁(e₃).

(Do not include buying a similar security at the beginning of the second or third periods.)

a) How many constraints and decision variables does the subproblem have?

b) The constraints of the subproblems are homogeneous (i.e., zero righthand sides). Suppose that purchasing 1 unit of this security, b1 = 1, gives a positive rate of return. What can be said about purchasing b1 units of this security? c) Formulate a dynamic-programming model to solve this subproblem, assuming that b1 = 1. Show that this solution determines a ray of the subproblem.