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Slack Variables For The Respective Constraints
Slack Variables For The Respective Constraints
Table of Contents
Order ID# 45178248544XXTG457 Plagiarism Level: 0-0.5% Writer Classification: PhD competent Style: APA/MLA/Harvard/Chicago Delivery: Minimum 3 Hours Revision: Permitted Sources: 4-6 Course Level: Masters/University College Guarantee Status: 96-99% Instructions
Slack Variables For The Respective Constraints
Consider the following problem.
Maximize Z = 2x1 + 7x2 – 3x3,
subject to
x1 + 3x2 + 4x3 ≤ 30
x1 + 4x2 – x3 ≤ 10
and
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.
By letting x4 and x5 be the slack variables for the respective constraints, the simplex method yields the following final set of equations:
(0) Z + x2 + x3 + 2x5 = 20
(1) – x2 + 5x3 + x4 – x5 = 20
(2) x1 + 4x2 – x3 + x5 = 10.
Now you are to conduct sensitivity analysis by independently investigating the following change in the original model. For the follwoing change, use the sensitivity analysis procedure to revise this set of equations (in tableau form) and convert it to proper form from Gaussian elimination for identifying and evaluating the current basic solution. Then test this solution for feasibility and for optimality. If either test fails, reoptimize to find a new optimal solution.
Suppose that the right-hand sides of the functional constraints are changed to
30 + (6)θ (for constraint 1)
and
10 + (-4)θ (for constraint 2),
where θ can be assigned any positive or negative values.
Slack Variables For The Respective Constraints
Determine the lower and upper bounds of θ before this solution would become infeasible.
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Excellent Quality 95-100%
Introduction 45-41 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Literature Support 91-84 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Methodology 58-53 points
Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.
Average Score 50-85%
40-38 points More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.
83-76 points Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.
52-49 points Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.
Poor Quality 0-45%
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75-1 points Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.
48-1 points There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met
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Slack Variables For The Respective Constraints
