PART II. MODEL AND METHOD OF ANALYSIS 



One basic linear programming model was developed so that, through appro- 

 priate changes in the constraint vector and objective functions, many aspects of 

 the problem could be analyzed. 



The model consists of 132 equations and 218 activities. The activities include 

 water use, water pollution, water-pollution treatment, and transfer activities 

 from one use to another. The constraint equations include equations governing 

 the amount of water required or the amount of water used by an activity, the 

 pollution level created by the activity, and a water-flow account which con- 

 strains the amount of water in the river. The model is hydrologically tied to- 

 gether by the river-flow level and the constraints on coliform bacteria and bio- 

 chemical oxygen demand. 



In order to simplify data collection and to broaden the analysis, the Ashuelot 

 River basin was divided into three separate sections, each of which comprises a 

 geographic area within the basin. The boundaries for these areas were chosen by 

 locating logical separating points along the river for control points regulating 

 river-water flow and quality (see Figure 2.1). The downstream boundary of the 

 Northern Area is the United States Geological Survey's gauging point at Surry 

 Mountain Dam. All of the Ashuelot River basin north of that gauging station 

 that drains through the gauging station is included in the Northern Area. The 

 downstream boundary of the Central Area is Quality Control Point No. 16, 

 established by the New Hampshire Water Pollution Control Commission, and 

 located north of the junction of the south branch and the main river. The down- 

 stream boundary of the Southern Area is the confluence of the Ashuelot River 

 with the Connecticut River at Hinsdale, New Hampshire. 



Five configurations of the model were run. The first three represent the 

 Northern, Central, and Southern Areas individually. In the fourth configuration 

 the areas were combined, and the whole river basin constrained on the control 

 point at Hinsdale. In the fifth configuration the model represented the Lamprey 

 River in eastern New Hampshire (see Figure 1.1). 



The water-use patterns in the three areas of the model were quite different. 

 In the Northern Area the water was used primarily for recreation and rural 

 non-farm dwelling. In the Central Area, in addition to the recreation and rural 

 non-farm dwelling, there was considerable agricultural and forest activity, and 

 the largest urban area in the basin, the city of Keene. The Southern Area had 

 recreation, rural non-farm dwelling, some agriculture, and forest activity. The 

 primary distinguishing characteristic of the Southern Area was the existence of 

 industrial plants. These plants were located at separated points along the river 

 and used private water sources for processing. It is the existence of these indus- 

 trial plants that made the Southern Area the most difficult to model. 



2.1 Mathematical Model 



The model can be expressed in its most general mathematical formulation as 

 follows: 



