Better Products, Inc., manufactures three products on two machines. In a typical week, $40$ hours are available on each machine. The profit contribution and production time in hours per unit are as follows:

Category Product $1$ Product $2$ Product $3$

Profit$/$unit $$39$ $$51$ $$18$

Machine $1$ time$/$unit $0\mathrm{.}51\mathrm{.}51$

Machine $2$ time$/$unit $12\mathrm{.}51$