Joint Cost Allocation$-$Weighted Average Method

Konami Code Gaming produces two types of high$-$end gaming controllers, one with a casing made of a polymer that looks like walnut wood and another with a casing made with a polymer that looks like red oak. The casings are made through a joint production molding process that produces $258$ red oak casings and $344$ walnut casings at the split$-$off point. The polymer for the red oak casings requires twice as much cooling time as the polymer for the walnut casings, although all casings are removed from the joint molding process at the same time $($i$.$e$.,$ once the cooling for the red oak casings is complete$).$ The joint production process costs a total of $$6,500.$

Assuming the company allocates joint costs using the weighted average method based on the required cooling time of the two joint products, determine the amount of joint production costs allocated to each type of casing using the weighted average method.

$\backslash$table$[[$Joint Product,Allocation,$],[$Red oak casing,$$4,771\mathrm{.}84,x$