Find the Maximum Value of the Objective Function and Where $\ge$

question 261

Multiple Choice

Find the maximum value of the objective function and where it occurs, subject to the constraints:
Objective function:

Z = 5x + y

Constraints:

X $\ge$ 0
Y $\ge$ 0
X + 4y $\le$ 20
X + y $\le$ 18
2x + 2y $\le$ 21

• A)Maximum at (0, 5): 5
• B)Maximum at \(\left( \frac { 22 } { 3 } , \frac { 19 } { 6 } \right)\) : \(\frac { 239 } { 6 }\)
• C)Maximum at (0, 0): 0
• D)No maximum
• E)Maximum at \(\left( \frac { 21 } { 2 } , 0 \right)\) : \(\frac { 105 } { 2 }\)

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Definitions:

Standard Deviation

A measure that quantifies the spread or variability among a set of data points compared to the average, showcasing the extent to which these points diverge.

Sample Size

Sample size refers to the number of observations or data points collected from a subset of a larger population for the purpose of statistical analysis.

Finite Population Correction

An adjustment made to statistical calculations like the standard error when sampling from a finite population, to account for the decreased variability expected in such samples.

Population Size

The total number of individuals or units in the group or set being studied.