Airtight Manufacturing produces plastic cases that utility companies buy to protect electronic components on utility poles from weather damage. Airtight has recently developed better insulation for its protective case. The protective case currently used by utility companies has a 0.035 probability of failing in any given year. When a protective case fails, the utility company incurs a $600 repair expense. If this better insulation enables Airtight’s new protective case to have a 0.015 probability of failing any given year, then what is the value to a utility company of this better-insulation feature?

Question

BlackTom AI · Accepted Answer

We start by identifying the economics of the current and new protective case.
Original situation: probability of failure = 0.035 per year, repair expense = $600. The expected annual repair cost is 0.035 × $600 = $21.
New insulation: probability of failure = 0.015 per year, repair expense unchanged at $600. The expected annual repair cost becomes 0.015 × $600 = $9.
The value of the new insulation feature to the utility company is the reduction in expected annual repair costs: $21 − $9 = $12.
Now evaluate each answer option:
- $45: This would imply a reduction of $45 in expected annual costs, which is inconsistent with the calculated reduction of $12. It overstates the benefit and lacks grounding in the given probabilities and costs.
- $9: This number matches the new expected annual repair cost, not the savings from the insulation feature. It represents the post-change cost, not the benefit.
- $21: This is the original expected annual repair cost before the insulation improvement. It does not reflect any change due to the new insulation and thus is not the value of the feature.
- -$9: A negative value would imply the insulation increases costs by $9 annually, which contradicts the stated reduction in failure probability and the linear cost per failure.
- $12: This is the correct savings—the difference between the original and new expected costs—and represents the annual economic value of the insulation improvement to the utility.
In summary, the only option that aligns with the calculated reduction in expected annual repairs is the $12 figure, since the improvement lowers anticipated costs by 12 dollars per year.

MGT355H5 F LEC0101 Term Test 1

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