The Binding Constraints for This Problem Are the First and Second

question 55

Essay

The binding constraints for this problem are the first and second.
$$\begin{array} { l r } \operatorname { Min } & x _ { 1 } + 2 x _ { 2 } \\\text { s.t. } & x _ { 1 } + x _ { 2 } \geq 300 \\&2 x _ { 1 } + x _ { 2 } \geq 400 \\&2 x _ { 1 } + 5 x _ { 2 } \leq 750 \\&x _ { 1 } , x _ { 2 } \geq 0\end{array}$$
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:

Benzaldehyde

An aromatic aldehyde with a formula of C6H5CHO, known for its almond-like aroma.

Acetaldehyde

A volatile and colorless flammable liquid compound with a pungent odor, widely used in the chemical synthesis of various compounds.

Resonance Structures

Different Lewis structures for the same molecule that depict different possible arrangements of electrons without altering the positions of the atoms.

Compound Name

Refers to the systematic naming of a chemical substance in accordance with the rules of nomenclature.