> completely missing some elegant and profound beauty.

Requires some dynamic SQL to construct, but the beauty is that you can use the SQL engine for this solution:

select top 1 *

from (select

t1.id,t2.id,...,tn.id

,sum(t1.cost+t2.cost...+tn.cost) as total_cost

from join_options t1

cross join join_options t2

...

cross join join_options tn

group by t1.id,t2.id,...,tn.id) t0

order by

t0.total_cost