The Binding Constraints for This Problem Are the First and Second

Essay

The binding constraints for this problem are the first and second.
Min
x₁ + 2x₂
s.t.
x₁ + x₂ $\ge$ 300
2x₁ + x₂ $\ge$ 400
2x₁ + 5x₂ $\le$ 750
x₁ , x₂ $\ge$ 0
a.Keeping c₂ fixed at 2, over what range can c₁ vary before there is a change in the optimal solution point?
b.Keeping c₁ fixed at 1, over what range can c₂ vary before there is a change in the optimal solution point?
c.If the objective function becomes Min 1.5x₁ + 2x₂, what will be the optimal values of x₁, x₂, and the objective function?
d.If the objective function becomes Min 7x₁ + 6x₂, what constraints will be binding?
e.Find the dual price for each constraint in the original problem.