Inventory Microbucks Computer Company makes two computers, the Pomegranate II and the Pomegranate Classic, at two different factories. The Pom II requires $2$ processor chips, $16$ memory chips, and $20$ vacuum tubes, while the Pom Classic requires $1$ processor chip, $4$ memory chips, and $40$ vacuum tubes. Microbucks has in stock at the beginning of the year $500$ processor chips, $6,000$ memory chips, and $9,000$ vacuum tubes at the Pom II factory, and $150$ processor chips, $2,000$ memory chips, and $20,000$ vacuum tubes at the Pom Classic factory. It manufactures $50$ Pom IIs and $50$ Pom Classics each month.

Microbucks Computer Company, besides having the stock mentioned above, gets shipments of parts every month in the amounts of $110$ processor chips, $1,000$ memory chips, and $3,000$ vacuum tubes at the Pom II factory, and $60$ processor chips, $1,000$ memory chips, and $2,200$ vacuum tubes at the Pom Classic factory.

$($a$)$ What will the company's inventory of parts be after $6$ months?

$\backslash$table$[[,$Processor chips,Memory chips,Vacuum tubes$],[$Pom II factory,,,$],[$Pom Classic factory,,,$]]$

$($b$)$ When $($if ever$)$ will the company run out of one of the parts?

The company will run out of parts in $6$ months.

The company will run out of parts in $12$ months.

The company will run out of parts in $18$ months.

The company will run out of parts in $24$ months.

The company will never run out of parts.