1. Assuming we are given the formulation of a linear programming (LP) problem. To find the optimal solution of this LP problem, we are using the graphical method. if there is a point on the graph that satisfies all of the constraints at the same time, this point must be:

1. An optimal solution point.
2. At the intersection of the profit line and a constraint
3. A corner point.
4. At the intersection of two or more constraints.
5. At the intersection of the nonnegativity constraints
6. None of the above

2. Which of the following is true for all Linear Programming (LP) problems?

1. Every LP problem has an optimal or a feasible solution.
2. If an optimal solution exists, there will always be at least one at a corner.
3. A feasible solution to an LP problem must be a corner point of the feasible region.
4. A feasible solution to an LP problem must maximize or minimize the value of the objective function
5. All of the above.
6. None of the above

3. The constraints of a two-variable linear programming problem is stated here: X 1;Y 1;X + Y 9.

Which of the following statements regarding the (X, Y) points is NOT TRUE?

1. The optimal solution might be X=1, Y=8
2. The optimal solution might be X=4, Y=4
3. The optimal solution might be X=0, Y=9
4. The optimal solution might be X=8, Y=1
5. We need to know the objective function to make a better statement.
6. All of the above is TRUE

Please explain how you got the answers, thanks.