Optimization investigation: build, break and defend a certificate: changed case
Address this changed case in a fresh argument. Explain which earlier conclusions survive and which require new evidence. This is public practice with available guidance; it is not an untouched examination. Your responses and guidance exposure are stored separately from the main project.
Submit your own certificate for checking
This checker verifies supplied rational vectors; it does not search for a solution or generate an optimal certificate. Write your prediction and derivation in the milestone before requesting feedback. All examples are synthetic continuous linear programs unless the separate integer-transfer argument says otherwise.
Maximize 5x + 4y with x,y ≥ 0. All rows use A x ≤ b. The selected problem is Main model: budget 8.
Resource 1: 2x + y ≤ b; row coefficients (2, 1), right side 8.
Resource 2: x + 2y ≤ 8; row coefficients (1, 2), right side 8.
Quantity cap: x ≤ 3; row coefficients (1, 0), right side 3.
Optimality input: kind, a two-entry primal vector and a dual vector with 3 entries in this row order. Infeasibility input: kind and a multipliers vector with 3 entries. Every number is a quoted integer or fraction such as "8/3". Negative entries are accepted for diagnosis; feasibility still requires the specified signs.
Exact input bounds: numerator magnitude at most 1000, positive denominator at most 1000. Decimals, exponents, extra keys and incorrect vector lengths are rejected. The initial zero vectors only demonstrate the format.
0 of 12 audit records used. Failed parsing also counts as an audit attempt.
Retain the dossier before navigating or reloading
The at-most-12 submitted records are immutable within this temporary session. They are not automatically saved to your project. Download or copy the report, identify its filename in the relevant milestone, and retain both failed and repaired certificates. The ordinary project response/revision fields below are saved through the existing local progress system. Public feedback and supplied solution exposure are practice, not an untouched assessment.
Copyable full audit record (0 entries)
For integer transfer, a certified continuous branch optimum supplies a bound; proving that the branches cover every integer feasible point is your separate mathematical obligation. Reusing an old certificate after a changed row or right side requires a new audit.
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0 of 1 transfer tasks have recorded responses. This counts submissions, not quality, independent review or project mastery.
Changed domain: certify the integer decision
Return to b=8 but require x,y to be nonnegative integers. Produce a fresh report section: explain why the continuous certificate with value24 does not certify an integer optimum; find an integer feasible incumbent; partition all possible integer x into x≤2 and x≥3; derive an exact continuous relaxation certificate for each branch using the checker’s additional row. Prove branch coverage and combine the bounds with the incumbent. Independently enumerate the bounded integer rectangle as a cross-check, retaining all20 candidate checks and distinguishing them from a general integer-programming method. Report source/feedback exposure and actual review separately.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Review, defend and revise
Ask a reviewer to examine the complete reasoning, reproduce selected results and pose an unfamiliar case. Record their feedback against the specific revision discussed. Reviewer labels are entered locally and do not verify identity or judgment. A complete set of text submissions does not certify an independently defended investigation.
