$3-71.$ A company that operates $10$ hrs a day manufactures three products on three processes.

The following table summarizes the data of the problem:

Minutes per unit

Product

Process $1$

Process $2$

Process $3$

Unit price

$1$

$2$

$3$

$10$

$5$

$6$

$6$

$8$

$9$

$8$

$10$

$12$

$$4\mathrm{.}50$

$$5\mathrm{.}00$

$$4\mathrm{.}00$

$($a$)$ Determine the optimal product mix.