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 240ib.the usage rates of the raw material are 2 ib per unit of a and 4 ib per unit of b. the profit units for a and b are 20$ and 50$ , respectively. determine the optimal product mix for the company.