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:

Nurturant-responsible

A social and psychological concept emphasizing the need for individuals to be caring and responsible toward others.

Authoritarian-aggressive

A behavior pattern characterized by a tendency to obey strict rules or authority figures with an inclination towards aggressive reactions against perceived threats or disobedience.

Sociable-intimate

The desire or tendency of an individual to engage in close and friendly relationships.

Dependent-dominant

A term that doesn't correspond to a well-defined concept in the provided context, potentially relating to dynamics within relationships or systems where one entity is dependent yet holds sway or influence over others.