Northern Company processes $100$ gallons of raw materials into $75$ gallons of product GS$-50$ and $25$ gallons of GS$-80.$ GS$-50$ is further processed into $50$ gallons of product GS$-505$ at a cost of $$3,500,$ and GS$-80$ is processed into $50$ gallons of product GS$-805$ at a cost of $$2,000.$

The production process starts at point $1.$ A total of $$20,000$ in joint manufacturing costs are incurred in reaching point $2.$ Point $2$ is the split$-$off point of the process that manufactures GS$-50$ and GS$-80.$ At this point, GS$-50$ can be sold for $$350$ a gallon, and GS$-80$ can be sold for $$70$ a gallon. The process is completed at point $3$products GS$-505$ and GS$-805$ have a sales price of $$510$ a gallon and $$150$ a gallon, respectively.

Allocate the joint product costs and then compute the cost per unit using each of the following methods: $(1)$ physical measure, $(2)$ sales value at split$-$off, and $(3)$ net realizable value.

Calculations plz$.$