Consider the following linear programming problem:
Min 4 X1 + 3 X2 + 6 X3
S,t 1 X1 + 0.5 X2 +1 X3>= 15
2 X2+ 1 X3 >= 20
1 X1+ 1X2 + 2 X3 >= 20
X1 X2 X3 >= 0
a. Write the dual problem.
b. Solve the dual.
c. Use the dual solution to identify the optimal solution to the original primal problem.
d. Verify that the optimal values for the primal and dual problems are equal.