Shell provides different lubricants, in $55$L drums, per delivery, to companies $A,B,$ and $C,$ as shown in

the table.

The cost price per drum of Gadus, Morlina, and Omala are P $6,000,P10,000,$ and $P12,000$ respectively

$($a$)$ Form two matrices, $P$ and $Q,$ such that the elements of the matrix product $PQ$ will show the total cost price

of the lubricants delivered to each company. Find the product of $PQ.$

$($b$)$ For the first quarter, Company A$,$ B$,$ and C$,$ received two, three, and four of such deliveries. By further

matrix multiplication. Determine the total quantity of drums per lubricant delivered.