Farmer Co$.$ produces two products, basic and deluxe, with unit contribution margins of $$13$ and $$21,$ respectively. Each product must spend time on a special machine, which is a constrained resource and can provide a maximum of $18,000$ hours of machine time per year. The basic product requires $12$ minutes of machine time and the deluxe product requires $30$ minutes of machine time. If the company can sell all the units it can produce of either product $($i$.$e$.,$ there is no demand constraint$),$ then what is the profit$-$maximizing product mix?

$18,000$ basic; $0$ deluxe

O basic; $9,000$ deluxe

$40,000$ basic; $20,000$ deluxe

$90,000$ basic; $0$ deluxe

$$ None of the above