Joint Cost Allocation$-$Physical Units Method

Medieval Blacksmith Co$.$ produces two types of decorative swords, a broadsword and a longsword. The swords are made through a joint production process that ultimately produces $21$ broadswords and $9$ longswords and costs a total of $$4,200$ per batch. After the split$-$off point, each type of sword goes through an additional crafting process before it is sold. The additional production process of the broadsword costs $$21$ per sword, after which it is sold for $$182$ per sword. The additional production process of the longsword costs $$26$ per sword, after which it is sold for $$142$ per sword.

Determine the amount of joint production costs allocated to each type of sword using the physical units method.

$\backslash$table$[[$Joint Product,Allocation$],[$Broadsword$,$$