1) Max Zx+ 3x2 s.t. 2x1 + 4x2 14 6x1 + 2x2 12 2) Max Zx+X2 s.t. 2x1 + 4x2 14 6x1 + 2x2 12 3) Max Z=4x1 + x2 s.t. 2x + 4x2 14 6x1 + 2x2 12 x; 0 Note: In problems 1, 2, and 3, the constraints are the same. This means the feasible regions are the same. The only difference is in the objective function. When you solve the three problems, go back and study the coefficients of the variables in the objective function of each problem. These represent the profit contributions of products x; and x2 in each problem. Try to understand intuitively why the optimal solution is changing for each problem (at a different corner point). 1) Max Zx+ 3x2 s.t. 2x1 + 4x2 14 6x1 + 2x2 12 2) Max Zx+X2 s.t. 2x1 + 4x2 14 6x1 + 2x2 12 3) Max Z=4x1 + x2 s.t. 2x + 4x2 14 6x1 + 2x2 12 x; 0 Note: In problems 1, 2, and 3, the constraints are the same. This means the feasible regions are the same. The only difference is in the objective function. When you solve the three problems, go back and study the coefficients of the variables in the objective function of each problem. These represent the profit contributions of products x; and x2 in each problem. Try to understand intuitively why the optimal solution is changing for each problem (at a different corner point).