Using the accounting equation, show the following transactions:

$($a$)$ Investment of cash, $$45,000.$

$($b$)$ Purchase merchandise from Dairyman's Co$-$op on account $$12,000.$

$($c$)$ Payment of $$6,000$ on account to Dairyman's Co$-$op$.$

$($d$)$ Sale for cash of merchandise costing $$3,000$ for $$4,500.$