The Binding Constraints for This Problem Are the First and Second

question 47

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.

---

Definitions:

Tire Slip Rate

The ratio of the difference between the wheel's rotational speed and the vehicle's speed to the vehicle's speed, indicative of traction loss.

Slip

The difference in speed between two interacting surfaces in relative motion, often referring to tires losing grip on the road.

Hydraulic Power Brake Booster

A device that uses hydraulic pressure to assist in the application of the vehicle's brakes, reducing the effort required by the driver.

Hydraulic Assist

An external power brake assist system that uses hydraulics, typically from the power steering system to a hydraulic power brake booster.