Chem Labs uses raw materials I and II to produce two domestic cleaning solutions, A and B. The daily availabilities of raw materials I and II are 100 and 120 units, respectively. One unit of solution A consumes 0.3 unit of raw material I and 0.6 unit of raw material II, and one solutions B uses 0.5 unit of raw material I and 0.8 unit of raw material II. The profits per unit of solutions per unit of solutions A and B are $8 and $10, respectively. The daily demand for solution A lies between 30 and 150 units, and that for solutions B between 40 and 200 units. Find the optimal production amounts of A and B.
Determinate the decision variables, objective Function and Constraint.