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 < 750
x₁ ,x₂ > 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.