50 1. Consider the following LP model: max 2 = 3x₁ + 2x2 s.t. 2x₁ + x₂ ≤ 100, x₁ + x₂ ≤ 80, *₁ ≤ 40, x1, x₂ > 0. (a) Write the dual of the above model. (b) Solve either primal or dual problem with a technique of your choice. Then, show that the optimal objective function values of primal and dual problems are equal. Note that you shouldn't solve both problem from scratch.