Solve the Standard Minimization Problem Using Duality $c = 4 s + 7 t + 9 u$

question 25

Multiple Choice

Solve the standard minimization problem using duality.
Minimize $c = 4 s + 7 t + 9 u$
Subject to $\begin{array} { l } s + 2 t + 2 u \geq 60 \\2 s + t + 3 u \geq 60 \\s \geq 0 , t \geq 0 , u \geq 0\end{array}$

• A) \(c = 140\) , \(s = 0\) , \(t = 20\) , \(u = 0\)
• B) \(c = 80\) , \(s = 20\) , \(t = 0\) , \(u = 0\)
• C) \(c = 220\) , \(s = 20\) , \(t = 20\) , \(u = 0\)
• D) \(c = 260\) , \(s = 20\) , \(t = 0\) , \(u = 20\)
• E) \(c = 320\) , \(s = 0\) , \(t = 20\) , \(u = 20\)

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Definitions:

Fully Employed Economy

A situation where all available labor resources are being used in the most economically efficient way, with minimal unemployment.

Cyclical Unemployment

Unemployment that results from business cycle fluctuations and the imbalances in supply and demand that arise in the economy over time.

Discouraged Workers

Individuals who are not actively looking for work because they believe no jobs are available for them or there are no jobs for which they would qualify.

Cyclical Unemployment

A type of unemployment that corresponds with the cyclical trends in growth and production that occur within the business cycle.