A workshop is divided into three zones (A, B, C). The annual probability of a fire in each zone and the corresponding potential damage are:

- Zone A: $p_A = 0.02$, damage = $\₦200{,}000$.
- Zone B: $p_B = 0.01$, damage = $\₦500{,}000$.
- Zone C: $p_C = 0.03$, damage = $\₦150{,}000$.

Installing a fire‑suppression system in a zone costs $\₦30{,}000$ and reduces the fire probability in that zone by 80 % (i.e., the new probability becomes 20 % of the original). With a budget that allows installation in at most two zones, which zones should be equipped with the system to achieve the greatest reduction in expected annual fire loss?

Question

A workshop is divided into three zones (A, B, C). The annual probability of a fire in each zone and the corresponding potential damage are:

- Zone A: $p_A = 0.02$, damage = $\₦200{,}000$.
- Zone B: $p_B = 0.01$, damage = $\₦500{,}000$.
- Zone C: $p_C = 0.03$, damage = $\₦150{,}000$.

Installing a fire‑suppression system in a zone costs $\₦30{,}000$ and reduces the fire probability in that zone by 80 % (i.e., the new probability becomes 20 % of the original). With a budget that allows installation in at most two zones, which zones should be equipped with the system to achieve the greatest reduction in expected annual fire loss?

Accepted Answer

Install the system in zones B and C.

City Guilds Model Questions Vol1 2019 Engineering Question 35

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