The Binding Constraints for This Problem Are the First and Second

question 33

Essay

The binding constraints for this problem are the first and second.
Min
x₁ + 2x₂
s.t.
x₁ + x₂ ≥ 300
2x₁ + x₂ ≥ 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.

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Definitions:

Pivot

A point of rotation or the act of rotating around a particular point, often used metaphorically to describe a shift in strategy or position.

Hyaluronic Acid

Mucopolysaccharide made up of alternating β-(1,4)-linked residues of hyalobiuronic acid, forming a gelatinous material in the tissue spaces and acting as a lubricant and shock absorbent generally throughout the body.

Synovial Fluid

A viscous liquid located within joint cavities, providing lubrication to reduce friction between articulating bones.

Hyaline Cartilage

A type of connective tissue found in various parts of the body including the nose, trachea, and articular surfaces, providing support and flexibility.