Min 2x1+x2+x3
5x1+2x2+7x3 = 420
3x1+2x2+5x3 >= 280
x1,x2 >= 0
a) Write the dual of the above primal LP
b) solve the primal problem with a computer software, write down optimal solution and optimal objective function value. Also write down the shadow prices (dual prices) of the primal constraints.
c) solve the dual problem and write down optimal solution of the dual problem and optimal objective function value. Also write down the shadow prices (dual prices) of the primal constraints.
d) Compare the solutions of the primal and dual problems. What do you observe?
e) Check whether the complementary slackness equations are held.