A company manufactures two products X and Y whose profit contributions are Rs$.$

$10$ and Rs$.20$ respectively. Product X requires $5$ hours on machine I, $3$ hours on machine II and

$2$ hours on machine III. The requirement of product Y is $3$ hours on machine I, $6$ hours on

machine II and $5$ hours on machine III. The available capacities for the planning period for

machine I, II and III are $30,36$ and $20$ hours respectively. Find the optimal product mix.