Trammel Chemical Company makes three products, DPX$,$ DEA, MNR$,$ what are joint products from the same materials. In a standard batch of $150,000$ products of raw materials, the company generates $40,000$ pounds of DPX$,60,000$ pounds of DEA and $50,000$ pounds of MNR$.$ A standard batch costs $$800,000$ to produce. The sales prices are $$9\mathrm{.}50,$ $$13\mathrm{.}50,$ and $$17\mathrm{.}50$ for DPX$,$ DEA, and MNR$,$ respectively. $($No credit will be given unless you show all you work$).$

a$.$ Allocate the joint product cost among the three final products using weight as the allocation base.

b$.$ Allocate the joint product cost among the three final products using market value as the allocation base. Round your figures to three decimals points.