Consider the following problem. Maximize Z = x1 - 3x2 + 2x3 , subject to 2x1+ 2x2 - 2x3 =0, x3>=0 (a) Construct the dual

Consider the following problem.

Maximize Z = x1 - 3x2 + 2x3 ,

subject to

2x1+ 2x2 - 2x3 <= (resource1)

-x2 + 2x3 <=4 (resource 2)

and

x1>=0, x2>=0, x3>=0

(a) Construct the dual problem for this primal problem.

(b) Solve the dual problem graphically. Use this solution to identify the shadow prices for the

resources in the primal problem.

(c) Confirm your results from part (b) by solving the primal problem automatically by the

simplex method and then identifying the shadow prices.