Question: max (3 points) For this LP z= -2.21 x2 + 23 s.t. X 1 + x2 + x3 X2 + 23 21 + 23 2

max (3 points) For this LP z= -2.21 x2 + 23 s.t.

max (3 points) For this LP z= -2.21 x2 + 23 s.t. X 1 + x2 + x3 X2 + 23 21 + 23 2 =1 21, 22, 23 > 0 write down the duality table and then answer the following questions about the dual: (1) how many decision variables are there? Yi, ... , Ym with m = (2) Fill in the subscripts for the yi's that are each of > 0; 0 we have and for urs , for ;(c)=: enter a, b or c ; (4) the second constraint of the dual has which inequality sign? (a) ;(C)=: enter a, borc (5) Rowo of the optimal Primal tableau is: z 22 23 S1 a3 rhs 11 4 e2 1 a 2 M 1 1 0 0 0 M + 2 2 Read y = [y y2 y3] CByB-1 from the optimal tableau and knowing that y is dual optimal and that y b = = , the value of is

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