Suppose a treacherous stretch of road winds through Deadman's Canyon for 5 miles.A highway department study estimates that better lighting would reduce the traffic fatality rates as follows: $\begin{array}{ccc}
\text { Number of lights } & \text { Estimated deaths per year } & \text { Total installation cost (in millions) } \
0 & 3 & \$ 0 \mathrm{~m} \
1 & 2 & \$ 3 \mathrm{~m} \
2 & 1.5 & \$ 7 \mathrm{~m} \
3 & 1.2 & \$ 12 \mathrm{~m} \
4 & 1 & \$ 18 \mathrm{~m} \
5 & 0.9 & \$ 25 \mathrm{~m}
\end{array}$
The first light is estimated to reduce the fatality rate by ___ at a marginal cost of $__ per life saved.

Question

Quizplus · Accepted Answer

The first light is estimated to reduce the fatality rate by 2-1 = 1 at a marginal cost of $3m - $0 = $3m per life saved. The second light would reduce the fatality rate by 1-1.5 = -0.5, which means it would actually increase the fatality rate. Therefore, installing the first light is the best choice as it reduces the fatality rate at a reasonable cost.

Suppose a Treacherous Stretch of Road Winds Through Deadman's Canyon