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 prices of the peices minus the cost of making the cut. (a) Give a dynamic-programming algorithm to solve this modified problem, including the math ematical expression for the maximum revenue and the pseudocode (b) Show the maximum revenue r, and the optimal size s of the first piece to cut off, when c 1 and lengthi 234 567 8910 price p 45 9 10 12 15 18 19 20