A company manufactures three products each of which requires certain amounts of three raw materials as well as labour. The matrix R summarizes the requirements per unit of each product.

Raw material Labour Product

$((1$&$2$&$3$& $6$@$2$&$3$&$2$& $8$@$4$&$2$&$5$& $4))($A@B@C$)$

Raw material requirements are stated in pound per unit and labour requirements in hours per unit. The raw materials costs $$2,$ $$8$ and $$2\mathrm{.}50$ respectively. Labour costs are $$8$ per hour. Assume $800,2000,$ and $600$ units of product A$,$ B$,$ C are to be produced.

Required

Perform matrix multiplication where compute total quantities of the four resources required to produce the desired quantity of products A$,$ B$,$ and C$.$

Using your answer from part a$,$ perform a matrix multiplication which calculates the combined total cost of production.