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.

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Definitions:

Brain Volume

The total space occupied by the brain, typically measured in cubic centimeters (cm³) or milliliters (mL), which can be indicative of various health conditions or cognitive capabilities.

Astrocyte

A type of supportive glial cell in the brain and spinal cord that helps maintain the barrier between blood and brain and provides nutrients to nervous tissue.

Lacunae

Small spaces or cavities within bone or cartilage tissue that house cells, such as osteocytes in bones.

Osteocytes

Mature bone cells embedded within the bone matrix that play a key role in maintaining bone tissue.