03/ The following linear programming problem deseribed the manufacturing two products (X, & Xx) by using two raw materials (R & Ra); Max. Z-1.5X, + Xx Subject to: 2x +X, 55 (Constraint of raw material R) X1 + X2 34 (Constraint of raw material Rz) X 2 (Demand for product X) X, Xx20 1. By using the Graphical Analysis, find the range of price for product X, (1.5) which can change in objective function and the current optimual basis will remain optimal. 2- By using the Algebraic Analysis, find whether a change in the right-hand side for constraint of raw material R., (5), and the current basis remains optimal. 3. By using the Simplex Method, find whether a change in the right-hand side for constraint of raw material Ry, (4), and the current basis remains optimal, where the optimal simplex tableau is as follows. (20 Marks) Ci B.V. X X2 S S; K 1.5 X 1 X2 0 1 - 1 2 2 Sj -1 1 1 Z 0 0.5 0.5 4.5 SA 1 1 -1 0 0 0 10 - 1 0 0 0 0