Solve the Standard Minimization Problem Using Duality $c = 6 s + 2 t$

question 131

Essay

Solve the standard minimization problem using duality.

Minimize $c = 6 s + 2 t$
subject to $$\begin{array} { l } s + t \geq 9 \\6 s + t \geq 24 \\s \geq 0 , t \geq 0\end{array}$$
After using the simplex method for dual problem to arrive at the tableau below, what is the maximum value for c
$\quad \quad x\quad y\quad z \quad w \quad c$
$\left[ \begin{array} { c c c c c } 0&1&\frac{1}{5}&\frac{1}{-5}&0\\\frac{4}{5}\\1&0&\frac{1}{-5}&\frac{6}{5}&0\\\frac{6}{5}\\0&0&3&6&1\\30\end{array} \right]$

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Definitions:

Demand-Oriented

Demand-Oriented is an approach or policy focused on increasing consumer demand to stimulate production and economic growth.

Aggregate Supply

The overall quantity of goods and services that businesses in an economic system aim to sell within a certain period.

Classical Macroeconomic Theory

Classical macroeconomic theory is an economic framework that emphasizes the importance of free markets, suggesting economies are self-regulating systems that automatically adjust to achieve full employment.

Aggregate Supply

The total supply of goods and services available to a particular market from producers at different price levels in a given period.