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:

Semiconductor Material

Substances with electrical conductivity between conductors and insulators, vital in the fabrication of electronic devices.

Binary Coded

A method of representing numbers, letters, or commands using binary digits, typically for computing or digital communications.

Equivalent

Equivalent refers to being equal in value, function, or meaning, often used in mathematics, science, and engineering to describe interchangeable elements or units.

Reference Voltage (V-Ref)

ECU or ECM conditioned voltage (usually 5 volts DC) supplied to various sensors (such as thermistors, potentiometers) in vehicle electronic circuits. In most cases, a portion of the voltage is returned to indicate the status of the sensor.