Freeport Power and Light Comapany 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, 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 mid value 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 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.