Which point, or points, are local optima in this diagram? The dashed line represents the objective function, and the objective is to maximize the value of the objective function.

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BlackTom AI · Accepted Answer

To identify local optima on the diagram, consider points where the objective function (the dashed line or progression toward higher X1) cannot be improved by a small move around the point.
Option D: At D, the feasible path reaches a peak along the local direction of the objective function, and any small move away along the nearby contour does not increase the objective value. This behavior characterizes a local maximum in the local neighborhood.
Option E: Point E lies on a slope where moving slightly toward the interior of the feasible region could yield a higher objective value, or moving along the boundary could increase the objective. Therefore, E is not a local optimum because there exists a nearby direction that improves the objective.
Option F: Point F sits at a high point along the boundary where, within its neighborhood, all small displacements either reduce the objective or do not increase it. This satisfies the idea of a local optimum along the boundary path. Since F is not globally dominating but locally maximal relative to its neighbors, it qualifies as a local optimum.
Option D, F: Combining the observations for D and F, both points meet the local optimality condition in their respective local neighborhoods. They are distinct local peaks along the feasible boundary where no tiny move improves the objective value.
In summary, E fails to be a local optimum due to an adjacent direction offering improvement, while D and F each maintain a locally maximal objective value with respect to small perturbations within the feasible region.

QANT_620-VA1-2025SP-VR Final Exam

Which point, or points, are local optima in this diagram? The dashed line represents the objective function, and the objective is to maximize the value of the objective function.

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QANT_620-VA1-2025SP-VR Final Exam

Which point, or points, are local optima in this diagram? The dashed line represents the objective function, and the objective is to maximize the value of the objective function. ​ ​

View Explanation

Log in for full answers

Similar Questions

Best Decent Local Optima Solution's Objective:

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

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The CVP and break-even analysis are supported by a range of important assumptions. Which of the following is not an assumption of the CVP:

More Practical Tools for Students Powered by AI Study Helper

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Which point, or points, are local optima in this diagram? The dashed line represents the objective function, and the objective is to maximize the value of the objective function.