Apply dynamic programming to find the optimal sequence for solving the chain matrix multiplication problem. Compute the matrix table for the following matrices.

A = 5 x 10, B = 10 x 7, C = 7 x 20, D = 20 x 5, E = 5 x 15

Fill the table by computing the optimal solution for subproblems of smaller size, using the formula:

M[i][j] = min(M[i][k] + M[k+1][j] + (Ai-1 * Ak * Aj) for k in range(i,j))

where M[i][j] is the minimum number of scalar multiplications needed to multiply the chain of matrices from Ai to Aj, Ai-1 is the number of rows in matrix Ai, Ak is the number of columns in matrix Ak, and Aj is the number of columns in matrix Aj.

GIve the optimal sequence