Find the Minimum and Maximum Values of the Objective Function $z = 3 x + 4 y$

question 50

Multiple Choice

Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. Objective function: $z = 3 x + 4 y$ Constraints: $$\left\{ \begin{array} { l } y \geq 0 \\x - y \geq - 2 \\2 x + 3 y \geq 6 \\5 x + 2 y \leq 25\end{array} \right.$$

• A) \(\text { minimum } = 0 \text { at } ( 0,0 ) ; \text { maximum } = 29 \text { at } ( 3,5 )\)
• B) \(\text { minimum } = 9 \text { at } ( 3,0 ) ; \text { maximum } = 15 \text { at } ( 5,0 )\)
• C) \(\text { minimum } = 8 \text { at } ( 0,2 ) ; \text { maximum } = 27 \text { at } ( 3,5 )\)
• D) \(\text { minimum } = - 11 \text { at } ( 3,5 ) ; \text { maximum } = 15 \text { at } ( 5,0 )\)
• E) \(\text { minimum } = 8 \text { at } ( 0,2 ) ; \text { maximum } = 29 \text { at } ( 3,5 )\)

---

Definitions:

Diagonal Row

A series of elements positioned diagonally in a matrix or table, connecting one corner with the opposite corner.

Pearson's Product-moment Correlation Coefficient

A measure of the linear correlation between two variables X and Y, providing a value between +1 and -1 inclusive.

Frequency Distribution

A method for illustrating how often scores occur in groups called class intervals.

Frequency Polygon

A graphical representation of a frequency distribution that uses a continuous line to show the number of values that fall within a class interval.