1. Class work 1 Solution

2. Schematic Diagram Mr. Soomro 50 acre-feet Mr. Khatri 60 acre-feet Mango farm 35 acre-feet Wheat farm 30 acre-feet x1x1 x2x2 x3x3 x4x4

3. Mathematical Model Min z=5x 1 + 7x 2 + 6x 3 + 8x 4 »x 1 +x 3 -s 1 +R 1 >=35 » x 2 +x 4 -s 2 +R 2 >=30 »x 1 +x 2 +s 3 <=50 »x 3 +x 4 +s 4 <=60

4. Phase-I: Normalize Column R 1 and R 2 x1x1 x2x2 x3x3 x4x4 s1s1 s2s2 R1R1 R2R2 s3s3 s4s4 b w 0 R1R1 1010 0100035 R2R2 01010010030 s3s3 110000001050 s4s4 001100000160

5. x1x1 x2x2 x3x3 x4x4 s1s1 s2s2 R1R1 R2R2 s3s3 s4s4 b w1111 000065 R1R1 10100100035 R2R2 01010010030 s3s3 110000001050 s4s4 001100000160 R1R1 x1x1

6. x1x1 x2x2 x3x3 x4x4 s1s1 s2s2 R1R1 R2R2 s3s3 s4s4 b w01010 00030 x1x1 10100100035 R2R2 01010010030 s3s3 110000001050 s4s4 001100000160 R2R2 x4x4

7. End of Phase-I x1x1 x2x2 x3x3 x4x4 s1s1 s2s2 R1R1 R2R2 s3s3 s4s4 b w000000 000 x1x1 1010 0100035 x4x4 01010010030 s3s3 110000001050 s4s4 001100000160

8. Phase-II: Normalize x 1 column x1x1 x2x2 x3x3 x4x4 s1s1 s2s2 s3s3 s4s4 b z-5-7-6-800000 x1x1 101000035 x4x4 010100030 s3s3 1100001050 s4s4 0011000160

9. Phase-II: Normalize x 4 column x1x1 x2x2 x3x3 x4x4 s1s1 s2s2 s3s3 s4s4 b z0-7-8-5000175 x1x1 101000035 x4x4 010100030 s3s3 010101015 s4s4 0011000160

10. x1x1 x2x2 x3x3 x4x4 s1s1 s2s2 s3s3 s4s4 b z010-5-800415 x1x1 101000035 x4x4 010100030 s3s3 010101015 s4s4 010010130 s3s3 x2x2

11. x1x1 x2x2 x3x3 x4x4 s1s1 s2s2 s3s3 s4s4 b z0000-6-80400 x1x1 101000035 x4x4 0011 015 x2x2 010101015 s4s4 0000111145 Optimum Tableau

12. Buy from Mr. Soomro for mango farm = 35 acre-feet. Buy from Mr. Soomro for wheat farm = 15 acre-feet. Buy from Mr. Khatri for wheat farm = 15 acre-feet. Buy from Mr. Khatri for wheat farm = nothing Optimum buying scheme