Use parametric linear programming to find an optimal solution for the following problem as a function of θ, for 0 ≤ θ ≤ 30.
Maximize Z (θ) = 5x1 + 6x2 + 4x3 + 7x4,
Subject to


and
xj ≥ 0, for j = 1, 2, 3, 4.
Then identify the value of θ that gives the largest optimal value of Z (θ).