Consider a modification of the rod-cutting problem in which, in addition to a price pi for each rod, each cut incurs a fixed cost of c. The revenue associated with a solution is now the sum of the prices of the pieces minus the costs of making the cuts. Suppose we also had limit l_i on the maximum number of pieces of length i we are allowed to produce, for i=1,2,...,n. Write a dynamic program for this modified problem.