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###### Problem 4. Consider the following standard LP_max 2X1 3x2s.t_2x1 + Xz + X3 = 16 X1 + 3x2 ~ X4 = 20X1 + xz = 10 X1'- ~,X4201) Use big M method to solve this LP by adding three artificial variables, i.e-, to solve max 2X1 + 3xz M(a1 + 42 + 43)S.t_2x1 + Xz + X3 + 41 = 16 X1 + 3xz ~ X4 + a2 20 X1 + Xz + 43 = 10 X1' ,X4,C1,42,43 Z 0(20 points) 2) Use big M method to solve this LP by adding TWO artificial variables as follows max 2x1 + 3xz M(az + 43) S.t_ 2x1 +xz + X3 = 16X1 + 3x2 ~ X4 + 42

Problem 4. Consider the following standard LP_ max 2X1 3x2 s.t_ 2x1 + Xz + X3 = 16 X1 + 3x2 ~ X4 = 20 X1 + xz = 10 X1'- ~,X420 1) Use big M method to solve this LP by adding three artificial variables, i.e-, to solve max 2X1 + 3xz M(a1 + 42 + 43) S.t_ 2x1 + Xz + X3 + 41 = 16 X1 + 3xz ~ X4 + a2 20 X1 + Xz + 43 = 10 X1' ,X4,C1,42,43 Z 0 (20 points) 2) Use big M method to solve this LP by adding TWO artificial variables as follows max 2x1 + 3xz M(az + 43) S.t_ 2x1 +xz + X3 = 16 X1 + 3x2 ~ X4 + 42 = 20 X1 + Xz + @3 = 10 X1' ,X4,42,43 > 0

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