Determine the optimal mix of the two products.

$*2-9.$ A company produces two products, A and $B.$ The sales volume for $A$ is at least $80\%$ of the total sales of both A and $B.$ However, the company cannot sell more than $100$ units of A per day. Both products use one raw material, of which the maximum daily availability is $240lb.$ The usage rates of the raw material are $2lb$ per unit of $A,$ and $4lb$ per unit of $B.$ The profit units for A and $B$ are $$20$ and $$50,$ respectively. Determine the optimal product mix for the company.