1. ChemLabs 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 using the Graphical Method.
2. Solve the above problem using the Excel Solver.
3. Determine the optimum solution for each of the following LPs using the Simplex Method.
a. Maximize z = 2x1 - 4x2 + 5x3 - 6x4
Subject to
x1 + 4x2 -2x3 +8x4 <=2
-x1 +2x2+3x3+4x4 <=1
x1, x2, x3, x4 >= 0
b. Minimize z = x1 + 2x2 - 3x3 - 2x4
Subject to
x1 + x2 <=6
2x1 + x2 <=16
x1, x2 >= 0