Suppose you wished to determine what would happen if 2 more students were required from Jan-Apr and 1 more student was required from Sep-Dec.

Why could we not use the sensitivity report to figure out what would happen to the total cost if just the above changes were made to the model?

(Select all correct answers)

Question

Suppose you wished to determine what would happen if 2 more students were required from Jan-Apr and 1 more student was required from Sep-Dec.

Why could we not use the sensitivity report to figure out what would happen to the total cost if just the above changes were made to the model?

(Select all correct answers)

BlackTom AI · Accepted Answer

To tackle this question, we first consider what the sensitivity (or shadow price) report in linear programming actually conveys and what it cannot do.
Option 1: 'Changing the Jan-Apr constrain would affect the Total intenships constraint, which is not allowed.' This statement asserts a specific structural consequence (affecting another named constraint) and then claims that such a change is not allowed. In LP sensitivity terms, changing the RHS of one constraint does not automatically alter other constraints in the model; the relationships among constraints are fixed, and a sensitivity analysis typically evaluates how far you can push a single constraint's RHS before the current optimal basis changes. The claim that it would affect a different named constraint and that this is not allowed is not generally accurate. The sensitivity report can indicate limits for a single constraint's RHS, but it does not inherently prohibit changes that would cascade through the system; rather, it would show when the current solution ceases to be optimal if that RHS is moved within its allowable range. Therefore this option introduces an incorrect certainty about the effect and about permissions, making it unlikely to be a correct statement.
Option 2: 'The sensitivity report does not apply for more than one change at a time.' This captures a key practical limitation: the classic sensitivity report provides allowable ranges for changes to RHS values (or objective coefficients) one at a time, holding all other data fixed. It does not provide a joint, simultaneous analysis of multiple RHS changes in a single reading. When you ask for what happens if both Jan-Apr and Sep-Dec RHS values are altered together, the sensitivity report does not automatically yield an exact new optimum without re-solving the model or performing scenario analysis. This makes the statement true as a description of the report’s scope.
Option 3: 'The right-hand-side of the Sep-Dec constraint cannot be changed.' This is a categorical restriction claim. In a standard sensitivity analysis, you would examine how much you can change any constraint’s RHS within its allowable range; whether a particular RHS can be changed at all depends on the model data and the current basis. The sensitivity report does not inherently state that an RHS cannot be changed; it instead provides the allowable range for such a change if one wishes to keep the current basis. Unless the model explicitly fixes that RHS, this blanket assertion is not universally correct, so this option is not reliably a true statement about the general usefulness or limitation of the sensitivity report.
Option 4: 'An increase of 2 is beyond the allowable change for Jan-Apr.' This is a precise claim about the magnitude of change being attempted relative to the allowable range for the Jan-Apr RHS. If the sensitivity report shows the allowable increase for that constraint’s RHS as less than 2, then this statement would be correct; if the allowable increase is 2 or more, then it would be incorrect. Because we don’t have the actual numerical allowable range here, this option depends on the specific model output. The ambiguity means this could be true or false depending on the data, but in a typical exam question about why the sensitivity report can’t be used for multiple changes, it’s common to see a statement like this used to flag whether a proposed single-change alteration lies within the allowable window.
Option 5: 'The change to the objective coefficient is outside the allowable range.' This option mentions the objective coefficient rather than an RHS change. The question asks about changing RHS values (Jan-Apr and Sep-Dec). Since the focus is on RHS changes, bringing up the objective coefficient is addressing a different sensitivity dimension. If the question strictly wants to know about RHS changes, this option is irrelevant to the scenario described. It would be incorrect to assert this without evidence that the objective coefficient is indeed being altered in the scenario. In any event, sensitivity analysis can separately consider RHS and objective coefficient changes; mixing them would be a separate analysis.

Summarizing the reasoning across options, the most consistent true statements with the typical limitations of the sensitivity report in this context are that it does not support analyzing multiple simultaneous changes (Option 2) and, depending on the model data, that a proposed increase may exceed the allowable range for a given constraint (Option 4). The other options either misstate how sensitivity analysis works or address aspects (like the impossibility of changing a RHS) that the standard report does not categorically assert.

COMM_V 190 101-104 2025W1 FlexHW14.COMM190.2025.W1 (optional — see syllabus)

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