The first two steps of the development of a dynamic programming algorithm for a problem are

step 1 describe the structure of the subproblem

step 2 find a recurrence for the optimal value of the subproblem in terms of smaller subproblems

Perform just these two steps for this problem listed below. Do not write (pseudo) code - just the subproblem and recurrence structure.

There is a small quantum computing consulting firm which in some months maintains a research facility in Frenchglen, OR (code F) and in others in Granite, OR (code G), and moves back and forth between these two cities (they can only afford to have one location operating at a time). This company wants to have the cheapest possible location plan - the two cities have different operating costs and these costs can change from month to month. We are given M. a fixed cost of moving between the two cities, and lists F = (fi, ,In) and G = (91, ,Yn). Here fi is the cost of operating out of Frenchglen in month i, and gi is the cost of being in Granite that month. Suppose that M 10, F (1.3.20.30), and G = (50. 20.24). If the location plan is (F. F. G, G), its cost will be l +3+10+ 2+4 20 On the other hand, the cost of the plan (G, G, F. G) is 50 + 20 + 10 + 20 + 10 + 4 114 The goal here is to (start to) devise a dynamic programming algorithm which, given M, F and G, determines the cost of the optimal plan. The plan can start in either city, and end in either city. Note that you will likely need two subproblems, which will be mutually recursive