Consider the following probem:
max 10x_1 + 20X_2
subject to the following constraints"
2x_1 + 6x_2 <= 100
8x_1 + 4x_2 <= 120
2x_1 <= 10
x_1, x_2 >= 0
1) write down the dual
2) given that x_1=10 and x_2 = 30 is an optimal solution to the primal, determine which constraints are tight and the value of the optimal solution
3) use the theory of complimentary slackness to find the optimal solution to the dual and tis optimal solution value.