Solve the below problem:
Q: Given the following primal LP:
(Primal) max 3x1+x2+5x3+3x4
subject to
3x1+x2+2x3=30
2x1+x2+3x3+x4>=15
2x3+3x4<=25
xi>=0, i=1,2,3,4
a) Find its dual:
b) Given the following optimal solution to (Primal), what is the optimal solution and objective function value for (Dual)? Your solution should include values for any slack and surplus variables in the dual. Use complimentary slackness rules to solve this problem.
LP OPTIMUM FOUND AT STEP 3
OBJECTIVE FUNCTION VALUE
1) 100.0000
VARIABLE VALUE
X1 0.000000
X2 0.000000
X3 15.000000
X4 8.333333
ROW SLACK OR SURPLUS
2) 0.000000
3) 38.333332
4) 0.000000