The Linear Programming Problem Has an Unusual Characteristic

question 12

Multiple Choice

The linear programming problem has an unusual characteristic.Select a graph of the solution region for the problem and describe the unusual characteristic.Find the minimum value of the objective function (if possible) and where it occurs. ​
Objective function:
​
Z = -x + 2y
​
Constraints:
​
X ≥ 0
Y ≥ 0
X ≤ 10
X + y ≤ 8
​

• A)​ The constraint x ≤ 10 is extraneous.Minimum at (0,8): 16
• B) The constraint x ≤ 10 is extraneous.Minimum at (8,0): -8
• C) The constraint x ≤ 10 is extraneous.No minimum.
• D) The constraint x ≤ 10 is extraneous.Minimum at (8,8): 8
• E) The constraint x ≤ 10 is extraneous.Minimum at (0,0): 0

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Definitions:

Categorical Variable

A type of variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or observation to a particular group or category.

Degrees of Freedom

The number of independent values or quantities which can vary in the analysis of statistical parameters.

Chi-square Statistic

A statistical measure used in tests of independence or goodness of fit, quantifying how expected counts compare to observed counts.

Null Hypothesis

The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.