Given the problem below. Consider that the profit for product 1 increases by half the amount of the decrease in the profit for product 2. Based on parametric linear programming, write out the appropriate model. Use SAS to find the optimal solution and the optimal objective value for the original form of the problem, report the range of theta fo which the optimal solution does not change, report the optimal solution and optimal objective value when theta = 2, report the optimal solution and optimal objective value when theta = 8, report the optimal solution when theta = 10, and report the optimal solution when theta = 20.

Maximize   Z = 8x₁ + 24x₂               

subject to

                        x₁ + 2x₂  ≤  10                  

                       2x₁ + x₂  ≤   10    

and

                        x₁ ≥ 0,    x₂ ≥ 0.