Solve the Standard Minimization Problem Using Duality $c = 4 s + t + 7 u$

question 64

Short Answer

Solve the standard minimization problem using duality.
​
Minimize $c = 4 s + t + 7 u$ ​
subject to $$\begin{aligned}s + t + u & \geq 50 \\2 s + t & \geq 25 \\t + u & \geq 25 \\s \geq 0 , t \geq 0 , u & \geq 0\end{aligned}$$ ​ $c =$ _________
​ $s =$ _________
​ $t =$ __________
​ $u =$ __________

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Definitions:

Pleural Pressure

This refers to the pressure within the pleural cavity, which is crucial in the mechanics of breathing.

Thoracic Wall

The part of the anatomy that forms a protective boundary around the thoracic cavity, which contains the lungs and heart; comprises the rib cage, spine, and sternum.

Diaphragm

A muscular and membranous partition separating the abdominal and thoracic cavities and plays a major role in breathing.

Dead Space

Areas in the respiratory system that do not participate in gas exchange, including the nasal cavities, trachea, and bronchi.