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:

Perfectly Elastic

describes a market situation in which the quantity demanded or supplied changes infinitely in response to any change in price.

Economic Profit

The difference between a firm's total revenues and its total costs, including both explicit and implicit costs, indicating overall profitability beyond breakeven.

Monopolistically Competitive

Describes a market structure where many firms sell products that are similar but not identical, allowing for significant competition but also some degree of market power for individual firms.

Advertising Campaign

A series of advertisement messages that share a single idea and theme aiming to market a particular product or service.