$4\mathrm{.}4$ Freeport Power and Light Company must select between two possible sites $($Free River and Loco Bend$)$ for the new power plant that it is building. The evaluation measures for this site selection are construction cost, in millions of dollars, and environmental impact, measured using a constructed scale with possible levels $0,1,2,3,$ and $4.$ Higher levels on this scale are less preferred. The single dimensional value function over cost is exponential over the range $$500$ million to $$1,000$ million, and the midvalue for this range is $$800$ million.

The value increment for improving from $4$ to $3$ on the environmental impact evaluation measure scale is the same as the value increment from $3$ to $2,$ and is also the same as the value increment from $1$ to $0.$ The value increment from $2$ to $1$ is twice as great as the value increment from $4$ to $3.$ The value increment for improving from $$1,000$ million to $$500$ million on the cost evaluation measure is the same as the value increment for improving from $4$ to $0$ on the environmental impact evaluation measure.

Siting the power plant at Free River will result in a cost of $$600$ million and an environmental impact of $3.$ Siting the plant at Loco Bend will result in a cost of $$850$ million and an environmental impact of $1.$

$($i$)$ Determine an additive value function over cost and environmental impact that is consistent with the information presented above.