Question No.2 (9 Marks) Consider the following Linear Programming Problem: Maximize 3X1+1X2+5X3+3X4 Subject to: 3X1+1/2+2X3=30 2X1+1X2+3x3+1X4 >=15 2X2+3X4=0 Following is the FINAL OPTIMAL SIMPLEX TABLEAU of the above L.P. Problem: 3 1 3 Cb IIS 5 Xixz X8 X4 S2 S3 AL AL RHS o 52/5/2/7/6 ololi1 3/21-1 a 32- 3 5 5 X3-312 12:10 100 120 15 3 3 101|0||0|1|o to 253 o Zj % 5 30 1 512 o 100 C;- Zj -91-7 -1010 0 15 2 / 0 -M c; o -11-5/2 - -M 2 2 Answer the following questions: (a) Write down the DUAL problem associated with the above PRMAL Problem. (b) Write down the complete solution of the Dual Problem. (c) Compute the ranges of coefficient of variable X3 within which the optimal basis will not change. (d) Compute the ranges of Right Hand Side of constraint number 1 (i.e. 30) within which the optimal basis will not change