Problem 4. 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. - Characterize the structure of an optimal solution. - Give a recursive solution. - Give a dynamic-programming algorithm to solve this modified problem. Use pseudo codes to write the procedure or procedures. By input p,n,c, your algorithm should finally print out the optimal cutting