35 ) (Marks 18) ( 17- 32) Q1 / B B ) () The following linear programming problem described the manufacturing two products (X1 & X2) by using two raw materials (R1 & R2); Max. Z=12X1 + 14X2 Subject to: 2X1 + 3X2 s 24 (Constraint of raw material R1). 2X, + X2 16 (Constraint of raw material R2) Xis 7 (Demand for product X:) X, X20 1- By using the Algebraic Analysis, find whether a change in the right-hand side for constraint of raw material R2, (16), and the current basis remains optimal. 2- Change this linear programming model to Dual Problem Model, and find the values of the variables and W by using the optimal simplex tableau which shown below. B.V. X X2 Si S2 S3 K X1 - 1/4 3/4 0 6 X2 0 1/2 -1/2 BA Sz 0 -3/4 35 ) (Marks 18) ( 17- 32) Q1 / B B ) () The following linear programming problem described the manufacturing two products (X1 & X2) by using two raw materials (R1 & R2); Max. Z=12X1 + 14X2 Subject to: 2X1 + 3X2 s 24 (Constraint of raw material R1). 2X, + X2 16 (Constraint of raw material R2) Xis 7 (Demand for product X:) X, X20 1- By using the Algebraic Analysis, find whether a change in the right-hand side for constraint of raw material R2, (16), and the current basis remains optimal. 2- Change this linear programming model to Dual Problem Model, and find the values of the variables and W by using the optimal simplex tableau which shown below. B.V. X X2 Si S2 S3 K X1 - 1/4 3/4 0 6 X2 0 1/2 -1/2 BA Sz 0 -3/4