Solve the Standard Minimization Problem Using Duality $c = 5 s + 2 t$

question 57

Multiple Choice

Solve the standard minimization problem using duality.
Minimize $c = 5 s + 2 t$
Subject to $$\begin{array} { l } 3 s + t \geq 30 \\s + t \geq 20 \\s + 3 t \geq 30 \\s \geq 0 , t \geq 0\end{array}$$

• A) \(c = 55\) , \(s = 5\) , \(t = 15\)
• B) \(c = 85\) , \(s = 15\) , \(t = 5\)
• C) \(c = 25\) , \(s = 5\) , \(t = 0\)
• D) \(c = 30\) , \(s = 0\) , \(t = 15\)
• E) \(c = 10\) , \(s = 0\) , \(t = 5\)

---

Definitions:

Valence Shell

Outermost orbital shell in an atom. The number of electrons in the valence plays a role in defining the electrical and physical characteristics of an element.

Chemical Properties

Characteristics of a substance that dictate how it reacts with other substances to form new products.

Electrical Resistance

The measure of the difficulty electrons face in flowing through a conductor, resulting in heat generation and energy dissipation.

Sectional Area

Sectional area refers to the area of a particular cross-section of a material or structural element, significant in physics and engineering for calculating stress, resistance, and other material properties.