Custom Carvings Company jointly produces wood chips and sawdust used in agriculture. The wood chips and sawdust are actually by$-$products of the company$$s core operations, but Custom Carvings accounts for them just like normally produced goods because of their large volumes. One jointly produced batch yields $2,000$ cubic yards of wood chips and $6,000$ cubic yards of sawdust, and the estimated cost per batch is $$27,300.$ However, the joint production of each good is not equally weighted. Given management estimates for how long it takes to make sawdust vs$.$ wood chips, a weight factor of $14$ is used for wood chips in the joint production process, and a weight factor of $2$ is used for sawdust.

Given this information, allocate the joint costs of production to each product using the weighted average method.