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) \(\text { minimum } = 8 \text { at } ( 0,2 ) ; \text { maximum } = 29 \text { at } ( 3,5 )\)

Differentiate between various statistical tests and identify the appropriate scenarios for their use.

Interpret the chi-square test results in terms of the difference between observed and expected frequencies.

Comprehend the principles of nonparametric statistics, including their assumptions and applications.

Recognize the relationship between sample size and the assumption of parametric statistics.

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