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 150 and 145 units, respectively. One unit of solution A consumes 0.5 unit of raw material I and 0.6 unit of raw material II, and one unit of solution B uses 0.5 unit of raw material I and 0.4 unit of raw material II. The profits 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 solution B between 40 and 200 units. Find the optimal production amounts of A and B.
Let A and B be the no. of units of A and B produced and X and Y be no. of raw materials I and II to be processed respectively.
The objective function is to maximize the profit, Z.
The objective function is subject to the following constraints
Is this formulation correct? If it is, how can one proceed from this point to find the maximum profit?