A factory must meet a demand of dt units at the end of each period t. The cost of producing xt units is ct(xt) in period t, where xt ∈ Qt and Qt is a finite set. The unit cost of holding inventory st...

A factory must meet a demand of dt units at the end of each period t.

The cost of producing xt units is ct(xt) in period t, where xt ∈ Qt and Qt

is a finite set. The unit cost of holding inventory st during period t is ht(st),

where st is the stock level at the beginning of the period. Any leftover stock

after n periods has a unit salvage value of v. Write a dynamic programming

recursion to find a production schedule that minimizes net cost while meeting

demand and maintaining st ≥ 0. Specify the boundary conditions, assuming

s1 = 0. Hint: Let xt be the control and st the state variable.