Business Analytics Quiz: Sensitivity And Scenario Analysis
10 questions · exam conditions
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Sensitivity And Scenario AnalysisQuestion 1 of 10

A profit-maximizing distribution model reports a shadow price of 400400 monetary units for each additional unit of warehouse capacity. The allowable increase in the capacity constraint is 1212 units. Management is considering adding 1515 units, and added capacity does not make any currently feasible solution infeasible.

Which interpretation is most appropriate?

Profit will increase by exactly 6,0006{,}000 monetary units because the shadow price applies to all 1515 added units.
Profit will increase by exactly 4,8004{,}800 monetary units because the last 33 units must have no economic value.
The first 1212 units predict a 4,8004{,}800 increase, but the model should be re-solved to value the last 33 units.
No part of the profit change can be estimated because the proposed increase exceeds the allowable range.
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Business Analytics Quiz

Business Analytics Quiz: Sensitivity And Scenario Analysis

Practice Sensitivity And Scenario Analysis in Business Analytics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Sensitivity And Scenario Analysis, giving you a quick way to practice the rules, question types, and explanations that matter most for Business Analytics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A profit-maximizing distribution model reports a shadow price of 400400 monetary units for each additional unit of warehouse capacity. The allowable increase in the capacity constraint is 1212 units. Management is considering adding 1515 units, and added capacity does not make any currently feasible solution infeasible.

Which interpretation is most appropriate?

  1. Profit will increase by exactly 6,0006{,}000 monetary units because the shadow price applies to all 1515 added units.
  2. Profit will increase by exactly 4,8004{,}800 monetary units because the last 33 units must have no economic value.
  3. The first 1212 units predict a 4,8004{,}800 increase, but the model should be re-solved to value the last 33 units. (correct answer)
  4. No part of the profit change can be estimated because the proposed increase exceeds the allowable range.
Explanation: Whenever you see a question involving shadow prices and constraint ranges in linear programming, your first instinct should be to check whether the proposed change falls within the allowable range — because shadow prices are only reliable predictors within that range. Here, the shadow price is $400\$400 per unit of warehouse capacity, and the allowable increase is 1212 units. This means the $400\$400 figure is valid for any addition up to 1212 units, predicting a profit gain of 12×400=$4,80012 \times 400 = \$4{,}800. Beyond that threshold, the basis of the optimal solution changes — a different constraint becomes binding, and the shadow price may shift entirely. For the remaining 33 units (units 13–15), the current model simply cannot tell you what happens without being re-solved. That's exactly what C captures: a reliable $4,800\$4{,}800 estimate for the first 1212 units, and an honest acknowledgment that the last 33 require a new solution. A is wrong because it blindly applies the shadow price to all 1515 units (15×400=$6,00015 \times 400 = \$6{,}000), ignoring that the allowable range ends at 1212. This is the most common trap — students forget the range condition entirely. B is wrong because it correctly computes $4,800\$4{,}800 but then invents a rule that the extra 33 units have zero value — the model doesn't say that; it simply says we don't know. D overcorrects by claiming nothing can be estimated, which discards the perfectly valid prediction for the first 1212 units. Your study tip: always split the proposed change into "within range" (shadow price applies) and "beyond range" (re-solve required). Never extend shadow price predictions past the allowable boundary.

Question 2

A marketing optimizer allocates the next available budget dollar to Channel X rather than Channel Y because estimated net values are 0.420.42 and 0.380.38 monetary unit per exposure, respectively. The estimated interval for Channel X from an A/B test is 0.340.34 to 0.500.50, while Channel Y's value is assumed to remain at 0.380.38 for this analysis. No contractual or capacity differences separate the channels.

What is the most defensible interpretation of the resulting prescription?

  1. Channel X is robustly preferred because its point estimate exceeds Channel Y's value by 0.040.04 monetary unit.
  2. Channel Y is robustly preferred because its value is closer to the midpoint of Channel X's estimated interval.
  3. The prescription is not robust because a plausible Channel X value falls below the 0.380.38 switching threshold. (correct answer)
  4. The allocation cannot be assessed because sensitivity analysis requires both channel values to have equal-width intervals.
Explanation: Whenever you see a question about choosing between two options based on estimated values, you should immediately ask: how confident are we in those estimates? This question tests sensitivity analysis and robustness of prescriptions — the idea that a recommendation is only as strong as its stability across plausible input values. Here, Channel X has a point estimate of 0.420.42, but the A/B test interval runs from 0.340.34 to 0.500.50. Channel Y is fixed at 0.380.38. The switching threshold — the value at which you'd prefer Y over X — is exactly 0.380.38. Notice that 0.340.34, the lower bound of Channel X's interval, falls below 0.380.38. This means a perfectly plausible realization of Channel X's true value would flip the decision in favor of Channel Y. The prescription to choose X is therefore not robust, making C the correct answer. Answer A is wrong because it treats the point estimate gap of 0.040.04 as conclusive evidence. A small gap combined with a wide interval is precisely when robustness breaks down, not when it holds. Answer B is wrong on two levels: "closeness to the midpoint" is not a meaningful decision criterion, and Y being near X's midpoint (0.420.42) does not make Y preferred — it just confirms the estimates are similar. Answer D is wrong because sensitivity analysis does not require symmetric or equal-width intervals on both sides. You can absolutely assess robustness when only one estimate has uncertainty. Study tip: When an interval straddles the switching threshold, the recommendation is never robust — regardless of where the point estimate sits. Train yourself to check whether competing values fall inside the confidence interval.

Question 3

An analyst performs one-way sensitivity analysis on a pricing recommendation. Over management's selected ranges, customer price elasticity produces the largest change in projected profit, competitor price produces the second-largest change, and fulfillment cost produces the smallest change. No probabilities were assigned, and inputs were varied one at a time.

Which conclusion is supported by this analysis?

  1. Customer price elasticity creates the greatest modeled profit variation over the specified ranges when other inputs are held constant. (correct answer)
  2. Customer price elasticity is the most likely input to deviate from its baseline assumption during the planning period.
  3. Collecting more elasticity data will necessarily create more business value than collecting data on either other input.
  4. A joint adverse movement in competitor price and fulfillment cost cannot outweigh the elasticity effect on projected profit.
Explanation: Whenever you see a question about sensitivity analysis, anchor yourself to what the technique actually does: it varies one input at a time across a specified range while holding all others constant, then measures the resulting output change. Critically, it assigns no probabilities and makes no claims about likelihood or joint effects. That's exactly why A is correct. The analysis shows that elasticity produces the largest modeled profit swing over management's chosen ranges when other inputs are fixed. That's a precise, limited claim — and it's exactly what one-way sensitivity analysis is designed to reveal. The word "modeled" and the phrase "specified ranges" are doing important work here; they keep the conclusion tightly scoped to what the method can actually support. B is wrong because sensitivity analysis says nothing about the probability that any input will deviate from its baseline. A variable can swing profits wildly if it moves, but still be very unlikely to move. Likelihood requires probability estimates, which this analysis explicitly lacks. C is wrong because the value of collecting additional data depends on decision context, cost of data collection, and how much uncertainty would actually be reduced — none of which sensitivity analysis addresses. High sensitivity to a variable doesn't automatically mean more data on it is worth pursuing. D is wrong because one-way sensitivity analysis tests inputs individually. It cannot rule out scenarios where two or more inputs move adversely at the same time. A joint adverse movement in competitor price and fulfillment cost could, in principle, exceed the elasticity effect — but this analysis simply wasn't designed to test that. Your study tip: when evaluating conclusions from sensitivity analysis, ask whether the claim requires probabilities, joint movements, or value-of-information reasoning. If yes, the method can't support it.

Question 4

A production model has two binding constraints. Machine capacity has a shadow price of 300300 monetary units per hour and an allowable increase of 2020 hours. Labor has a shadow price of 120120 monetary units per hour and an allowable decrease of 1212 hours. Management proposes adding 88 machine hours while removing 66 labor hours.

Using the simultaneous right-hand-side change rule, what is the best estimate of the change in optimal profit?

  1. A decrease of 3,1203{,}120 monetary units, because both resource changes should be treated as additional costs
  2. An increase of 720720 monetary units, because only the labor constraint remains within its allowable range
  3. An increase of 2,4002{,}400 monetary units, because the adverse labor change should be excluded from the estimate
  4. An increase of 1,6801{,}680 monetary units, because the combined proportional change is within 100%100\% (correct answer)
Explanation: When a linear program has multiple binding constraints, sensitivity analysis gives you shadow prices and allowable ranges for each constraint individually. The simultaneous right-hand-side change rule (also called the 100% rule) lets you check whether those shadow prices remain valid when several right-hand sides change at once: divide each proposed change by its allowable range in that direction, sum the ratios, and if the total stays at or below 100%, you can safely apply all shadow prices simultaneously. Here, the machine hours increase by 8 out of an allowable increase of 20, giving a ratio of 8/20=0.408/20 = 0.40, or 40%. Labor decreases by 6 out of an allowable decrease of 12, giving 6/12=0.506/12 = 0.50, or 50%. The combined ratio is 40%+50%=90%≤100%40\% + 50\% = 90\% \leq 100\%, so both shadow prices hold. The estimated profit change is: ΔProfit=(300)(+8)+(120)(−6)=2,400−720=+1,680\Delta \text{Profit} = (300)(+8) + (120)(-6) = 2{,}400 - 720 = +1{,}680 This confirms D as correct. Choice A misinterprets shadow prices as costs rather than marginal profit contributions — shadow prices represent value added, not expenses incurred. Choice B incorrectly checks each constraint in isolation and discards the machine-hours impact, which is not how the rule works. Choice C simply ignores the negative labor effect entirely, which overstates the benefit and violates the logic of the analysis. Your study tip: always check the 100% rule before applying shadow prices to simultaneous changes. If the sum of ratios exceeds 100%, the shadow prices may no longer be valid and the estimate is unreliable.

Question 5

A manufacturer can use either an automated process or a manual process for a one-year contract. At the expected volume of 14,00014{,}000 units, the automated process has a contribution margin of 2525 monetary units per unit and fixed costs of 180,000180{,}000 monetary units. The manual process has a contribution margin of 1515 monetary units per unit and fixed costs of 60,00060{,}000 monetary units. All other assumptions are identical.

Holding volume and the manual-process assumptions constant, by approximately how much can the automated process's contribution margin per unit decrease before the recommended process changes?

  1. 0.710.71 monetary unit per unit
  2. 1.431.43 monetary units per unit (correct answer)
  3. 2.142.14 monetary units per unit
  4. 8.578.57 monetary units per unit
Explanation: When two processes compete, the smarter question isn't just "which is better now?" but "at what point does the recommendation flip?" This is a sensitivity analysis problem — you're finding how much a key assumption can move before the current winner loses its advantage. Start by calculating each process's operating profit at 14,000 units. The automated process earns 25×14,000−180,000=170,00025 \times 14{,}000 - 180{,}000 = 170{,}000. The manual process earns 15×14,000−60,000=150,00015 \times 14{,}000 - 60{,}000 = 150{,}000. Automated wins by 20,00020{,}000. Now, let the automated contribution margin per unit drop by dd. The new automated profit becomes (25−d)×14,000−180,000(25 - d) \times 14{,}000 - 180{,}000. Set this equal to the manual profit and solve for the breakeven point: (25−d)(14,000)−180,000=150,000(25 - d)(14{,}000) - 180{,}000 = 150{,}000 350,000−14,000d−180,000=150,000350{,}000 - 14{,}000d - 180{,}000 = 150{,}000 170,000−14,000d=150,000170{,}000 - 14{,}000d = 150{,}000 14,000d=20,000  ⟹  d≈1.4314{,}000d = 20{,}000 \implies d \approx 1.43 So the automated process can lose approximately 1.431.43 monetary units per unit before the two processes tie — confirming answer B. Answer A (0.710.71) results from mistakenly dividing the profit gap by 28,00028{,}000 (doubling the volume), a arithmetic setup error. Answer C (2.142.14) comes from dividing 30,00030{,}000 — the fixed-cost difference — by 14,000 instead of the actual profit gap. Answer D (8.578.57) reflects dividing the full contribution margin difference (1010) by the contribution margin ratio, a conceptual mismatch. On sensitivity questions, always anchor yourself: find the current advantage in total dollars, then ask how much the variable must shift to erase that advantage.

Question 6

An aggressive product launch would earn 300300 monetary units in a high-demand scenario and lose 100100 in a low-demand scenario. A conservative launch would earn 180180 in high demand and 8080 in low demand. The estimated probability of high demand is currently 65%65\%.

By how many percentage points can the high-demand probability decrease before the two launch strategies become equally attractive on expected monetary value?

  1. 3.753.75 percentage points
  2. 2020 percentage points
  3. 1515 percentage points
  4. 55 percentage points (correct answer)
Explanation: When comparing two strategies using expected monetary value (EMV), the break-even probability is the point where both strategies yield identical expected returns. Whenever a question asks how much a probability can shift before two options become equally attractive, set their EMV expressions equal and solve. Let pp represent the probability of high demand. The EMV formulas are:
  • Aggressive: 300p+(−100)(1−p)=400p−100300p + (-100)(1-p) = 400p - 100
  • Conservative: 180p+80(1−p)=100p+80180p + 80(1-p) = 100p + 80
Setting them equal to find the break-even probability: 400p−100=100p+80400p - 100 = 100p + 80 300p=180300p = 180 p=0.60p = 0.60 So the two strategies are equally attractive at 60%60\%. Since the current probability is 65%65\%, the probability can decrease by 65%−60%=565\% - 60\% = 5 percentage points — confirming D is correct. Choice A (3.75 points) likely results from a setup error, such as misreading the payoffs or forgetting to account for the low-demand outcomes correctly when forming the EMV expressions. Choice B (20 points) is a significant overestimate — this might come from comparing only the high-demand payoffs (300−180=120300 - 180 = 120 vs. 100−80=20100 - 80 = 20) without properly solving the system. Choice C (15 points) may result from an arithmetic error mid-calculation, such as subtracting coefficients incorrectly. A useful habit: always write out both full EMV expressions before solving. Break-even analysis questions reward systematic setup — rushing to compare single payoffs without accounting for all outcomes is the most common trap here.

Question 7

A product has baseline annual demand of 100,000100{,}000 units, a price of 2020 monetary units per unit, and variable cost of 1212 per unit. In a recession scenario, demand falls by 15%15\%, price falls by 5%5\%, and variable cost per unit rises by 10%10\%. Fixed costs are unchanged.

What annual contribution should the analyst use for the recession scenario?

  1. 493,000493{,}000 monetary units after jointly applying all three scenario assumptions (correct answer)
  2. 580,000580{,}000 monetary units after applying only the revised unit economics
  3. 581,400581{,}400 monetary units after applying all percentages directly to baseline contribution
  4. 680,000680{,}000 monetary units after applying only the demand decline to baseline contribution
Explanation: Scenario analysis in business analytics requires you to apply all relevant changes simultaneously to their respective drivers — not mix and match, and not apply percentages to an already-derived figure. Here's how to build the recession contribution correctly. Start by adjusting each input: revised demand = 100,000×(1−0.15)=85,000100{,}000 \times (1 - 0.15) = 85{,}000 units; revised price = 20×(1−0.05)=19.0020 \times (1 - 0.05) = 19.00; revised variable cost = 12×(1+0.10)=13.2012 \times (1 + 0.10) = 13.20. The revised contribution margin per unit is 19.00−13.20=5.8019.00 - 13.20 = 5.80. Total contribution = 85,000×5.80=493,00085{,}000 \times 5.80 = \mathbf{493{,}000}, confirming answer A. Each distractor reflects a specific analytical error. B applies the revised unit economics (5.805.80 per unit) but forgets to adjust demand, using the baseline 100,000100{,}000 units: 100,000×5.80=580,000100{,}000 \times 5.80 = 580{,}000 — it ignores the volume impact entirely. C misapplies the percentages by operating on baseline contribution (100,000×8=800,000100{,}000 \times 8 = 800{,}000) rather than on the underlying drivers, then adjusting: applying −15%-15\%, −5%-5\%, and +10%+10\% directly to 800,000800{,}000 conflates margin-level and driver-level effects, producing 581,400581{,}400 — a methodologically flawed shortcut. D applies only the demand decline to baseline contribution (85,000×8=680,00085{,}000 \times 8 = 680{,}000), ignoring that price and cost conditions also change in the recession. The key study tip: in scenario analysis, always trace changes back to their source drivers — volume, price, and cost — recalculate each, then rebuild the metric from scratch. Applying percentages to derived figures like contribution is a classic exam trap.

Question 8

A company is comparing three facility plans under strong, moderate, and weak market scenarios. Plan A produces profits of 120120, 8080, and 3030 monetary units, respectively. Plan B produces 100100, 9595, and 5555. Plan C produces 7575, 8585, and 7070. Management does not trust scenario probabilities and chooses to minimize maximum regret.

Which plan should management select under the minimax-regret criterion?

  1. Plan A, because its maximum regret is 4040 monetary units
  2. Plan B, because its maximum regret is 2020 monetary units (correct answer)
  3. Plan C, because its maximum regret is 4545 monetary units
  4. No plan, because minimax regret requires probabilities for all scenarios
Explanation: Whenever you see a question about decision-making without reliable probabilities, think about regret-based reasoning. The minimax-regret criterion asks: for each plan, what is the worst-case "missed opportunity" — and which plan minimizes that worst case? To apply it, first build a regret table. For each scenario, find the best possible payoff, then subtract each plan's payoff from that best. Under strong markets, the best is 120120 (Plan A), so regrets are: A = 00, B = 2020, C = 4545. Under moderate markets, the best is 9595 (Plan B): A = 1515, B = 00, C = 1010. Under weak markets, the best is 7070 (Plan C): A = 4040, B = 1515, C = 00. Now take each plan's maximum regret — A = 4040, B = 2020, C = 4545 — and choose the minimum. That's Plan B at 2020, making B the correct answer. Choice A is tempting because Plan A dominates in the strong scenario, but its weak-market regret of 4040 is too costly — you'd be picking the plan with the second-worst maximum regret. Choice C is outright wrong; Plan C has the highest maximum regret (4545), the opposite of what minimax seeks. Choice D reflects a common misconception — minimax regret is specifically designed for situations without probabilities, so no probabilities are needed. Study tip: Always build the full regret table before comparing. A plan that looks attractive in one scenario can carry devastating regret in another — the maximum regret column is the only number that matters for this criterion.

Question 9

In a marketing optimization model, management plans to change two objective-function coefficients simultaneously. The first change uses 60%60\% of that coefficient's allowable increase, and the second uses 50%50\% of its coefficient's allowable decrease. Each change, considered separately, is within its reported allowable range.

What can the analyst conclude about whether the current optimal basis will remain optimal?

  1. It must remain optimal because each coefficient change is individually within its corresponding allowable range.
  2. It must change because the two percentage changes sum to more than 100%100\% under the objective-coefficient rule.
  3. It cannot be guaranteed by the sensitivity report because the combined percentages exceed 100%100\%. (correct answer)
  4. It will remain optimal because one coefficient increases while the other decreases, causing their effects to offset.
Explanation: Whenever a sensitivity analysis question involves simultaneous changes to multiple objective-function coefficients, you should immediately think about the 100% rule, not just the individual allowable ranges. The 100% rule states that if you make changes to multiple objective coefficients at once, the current optimal basis is guaranteed to remain optimal only if the sum of the percentages used of each coefficient's allowable range does not exceed 100%. Here, the first change uses 60%60\% of its allowable increase and the second uses 50%50\% of its allowable decrease. The combined percentage is 60%+50%=110%60\% + 50\% = 110\%, which exceeds 100%100\%. Therefore, the sensitivity report cannot guarantee the current basis remains optimal — the analyst must re-solve or use additional analysis. That makes C the correct answer. A is wrong because it confuses individual validity with simultaneous validity. Each change being within its own allowable range is a necessary but not sufficient condition when changes occur together. The 100% rule is precisely what closes this gap. B is wrong in its conclusion for the right reason. Yes, the percentages exceed 100%, but that does not mean the basis must change — it only means optimality can no longer be guaranteed. Exceeding 100% is a loss of certainty, not a proof of change. D is wrong because the direction of changes (one increase, one decrease) is irrelevant to the 100% rule. The rule applies regardless of direction; you sum the absolute percentages used. Study tip: Memorize the 100% rule as a two-step check — calculate each percentage used, sum them, and if the total exceeds 100%100\%, the sensitivity report gives no guarantee. Direction never cancels out the percentages.

Question 10

A retailer is stress-testing a proposed same-day delivery service. Historical evidence indicates that during economic downturns, order volume tends to decline while failed-delivery rates and fuel costs tend to rise. An analyst can either vary each input separately or construct internally consistent economic scenarios.

Why would scenario analysis generally be more informative than one-way sensitivity analysis for this decision?

  1. It assigns objective probabilities to the downturn automatically, allowing expected profit to be calculated without additional assumptions.
  2. It evaluates coherent joint changes in related inputs, revealing combined effects that separate one-way changes may miss. (correct answer)
  3. It isolates the causal effect of each input, ensuring that correlations among order volume, failures, and fuel costs are removed.
  4. It identifies the mathematically optimal delivery plan across every possible realization, eliminating the need for reoptimization.
Explanation: When a question contrasts two analytical methods, ask yourself what each method does and doesn't capture. Sensitivity analysis and scenario analysis solve different problems, and recognizing that distinction is the key here. One-way sensitivity analysis moves a single input — say, fuel costs — while holding everything else fixed. This is useful for ranking individual risks, but it creates an artificial picture when inputs move together in the real world. In the retailer's case, an economic downturn simultaneously pushes order volume down and pushes failed-delivery rates and fuel costs up. These shifts are correlated by a common cause. Scenario analysis builds internally consistent "stories" — for example, a recession scenario where all three variables move together — so you see the combined, realistic impact on profitability. That is precisely why B is correct: scenario analysis evaluates coherent joint changes in related inputs, surfacing effects that separate one-way shifts would miss or understate. A is wrong because scenario analysis does not automatically generate objective probabilities. Probabilities must still be assigned by the analyst, often subjectively, so you cannot calculate expected profit without additional assumptions. C describes the opposite of what scenario analysis does. Isolating causal effects and removing correlations is the goal of controlled experimentation or regression analysis — not scenario analysis, which deliberately preserves correlations by grouping inputs into realistic bundles. D is wrong because scenario analysis does not optimize anything. It evaluates outcomes under specified conditions; finding the optimal plan requires a separate optimization step. Study tip: On exam questions comparing analytical tools, match each tool to its defining feature — sensitivity analysis isolates, scenario analysis combines. That pairing will steer you to the right answer quickly.