A factory manufactures three products, A$,$ B$,$ and C$.$ Each product a certain number of hours of assembly and painting. There are $4,210$ total hours of assembly and $7,860$ total hours of painting available. The time requirements and profit per unit for each product are listed below.

$\backslash$table$[[$Product$,\backslash$table$[[$Assembly$],[($hours$)]],\backslash$table$[[$Painting$],[($hours$)]],\backslash$table$[[$Profit$],[($$$)]]],[$A$,3,9,$$$9$