Maximize and Minimize $p = 3 x - y$ Subject To $$\begin{array} { l } x + y \geq 3 \\x - y \leq 3 \\x - y \geq - 3 \\x \leq 12 , y \leq 12\end{array}$$

question 123

Multiple Choice

Maximize and minimize $p = 3 x - y$ subject to $$\begin{array} { l } x + y \geq 3 \\x - y \leq 3 \\x - y \geq - 3 \\x \leq 12 , y \leq 12\end{array}$$

• A)Max: \(p = 15\) , \(x = 9\) , \(y = 12\) , min: \(p = - 3\) , \(x = 0\) , \(y = 3\)
• B) Max: \(p = 27\) , \(x = 12\) , \(y = 9\) ,
• Min: \(p = 3\) , \(x = 0\) , \(y = 3\)
• C) Max: \(p = 27\) , \(x = 12\) , \(y = 9\) ,
• Min: \(p = - 3\) , \(x = 0\) , \(y = 3\)
• D) the feasible region is empty
• E) the objective function is unbounded

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Definitions:

AOA (Activity On Arrow)

A network diagram convention used in project management to represent activities on arrows and milestones on nodes.

Dummy Activities

Dummy activities are artificial tasks used in project scheduling (e.g., in a PERT or CPM diagram) to establish proper relationships among actual tasks, indicating dependencies without consuming resources or time.

Permanent Project Organization

An organizational structure designed to manage projects on a long-term basis, with dedicated teams and resources.

Matrix Organization

A flexible organizational structure where employees report to multiple managers, typically project manager and functional manager.