A company is considering two insurance plans with coverage and premiums shown in the table. $($For example, this means that $$50$ buys one unit of plan $A,$ consisting of $$10,000$ fire and theft insurance and $$180,000$ of liability insurance.$)$ Answer parts $($a$)$ and $($b$).$

$\backslash$table$[[,$Policy A$,$Policy B$],[$Fire$/$Theft$,$$$10,000,$$$15,000$