Four departments of a company need to order the following amounts of the same products.

$\backslash$table$[[$Department$,$Paper,Tape,Binders,$\backslash$table$[[$Memo$],[$Pads$]],$Pens$],[1,10,5,4,3,6],[2,6,3,2,2,9],[3,6,5,2,0,8],[4,0,2,6,6,6]]$

The unit price $($in dollars$)$ of each product is given below for two suppliers.

$\backslash$table$[[,$Supplier A$,$Supplier B$],[$Paper$,2,5],[$Tape$,1,1],[$Binders$,5,4],[\backslash$table$[[$Memo$],[$Pads$]],4,4],[$Pens$,1,1]]$

$($a$)$ Use matrix multiplication to get a matrix showing the comparative costs for each department for the products from the two suppliers.

$($b$)$ Find the total cost over all departments to buy products from each supplier. From which supplier should the company make the purchase?

A$.$ The total cost for supplier $A$ is $ and the total cost for supplier B is $$,$ so the company should make the purchase from supplier $B.$

B$.$ The total cost for supplier $A$ is $ and the total cost for supplier $B$ is $$,$ so the company should make the purchase from supplier $A.$