Question: please answer part C, D, E (3) (a) Find the dual of the following LP. (4 points) maxs.t.z=3x1+7x2+5x3x1+x2+x3+s1=502x1+3x2+x3+s2=100x1,x2,x3,s1,s20 (b) Optimal basis of the primal problem

please answer part C, D, E

(3) (a) Find the dual of the following LP. (4 points) maxs.t.z=3x1+7x2+5x3x1+x2+x3+s1=502x1+3x2+x3+s2=100x1,x2,x3,s1,s20 (b) Optimal basis of the primal problem is BV={x2,x3}. Write cBV,b and compute B1. (2 point) (c) Use feasibility condition, i.e., B1b0, and show for what range of b1 the current basis remains optimal (here b1=50). (1.5 point) (d) Use part (b) and find the shadow prices for the problem. (1 point) (e) Consider b1 changes to 45 . Use the shadow prices and find the new objective value. (1 point)

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