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 by hand.
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
4. Solve the Feed Mix Problem using the simplex method by hand
Minimize z = 2x1 + 3x2
Subject to x1 + 3 x2 ³ 15
2 x1 + 2 x2 ³ 20
3 x1 + 2 x2 ³ 24
x1, x2 ³ 0