b$.$ Determine the solution that will maximize profit.

A manager wants to know how many units of each product to produce on a daily basis in order to achieve the highest contribution to profit. Production requirements for the products are shown in the following table.

$\backslash$table$[[$Product$,\backslash$table$[[$Material $1],[($pounds$)]],\backslash$table$[[$Material $2],[($pounds$)]],\backslash$table$[[$Labor$],[($hours$)]]],[$A$,2,3,3\mathrm{.}2],[$B$,1,5,1\mathrm{.}5],[$C$,6,-,2\mathrm{.}0]]$

Material $1$ costs $$5$ a pound, material $2$ costs $$4$ a pound, and labor costs $$10$ an hour. Product A sells for $$80$ a unit, product B sells for $$90$ a unit, and product $C$ sells for $$70$ a unit. Available resources each day are $200$ pounds of material $1$;$300$ pounds of material $2$; and $150$ hours of tabor.