Tessellate S.T.E.M.S. (2019) - Computer Science - College - Set 2 - Objective Problem 4

Four matrices $M_1, M_2, M_3, M_4$ of dimensions $p \times q, q \times r, r \times s, s \times t$ respectively can be multiplied in several ways with different number of total scalar multiplications. For example, when multiplied as $(M_1 \times M_2) \times (M_3 \times M_4)$ , the total number of multiplications is $pqr + rst + prt$ . When multiplied as $((M_1 \times M_2 ) \times M_3 ) \times M_4$ , the total number of multiplications is $pqr + prs + pst$ .

If $p = 10, q = 100, r = 20, s = 5,$ and $t = 80$ , then the minimum number of scalar multiplications needed is

This problem is a part of Tessellate S.T.E.M.S (2019)