Optimal Location of WaterTreatment Plant Three towns - Appalachee, Hull, and Eastville - agree to share the cost of constructing a new Water treatment plant that will supply all three towns with water. The plant will be located on a nearby river. The main concern in deciding where to locate the plant is the total cost of installing the supply pipelines to all three towns and building an access road from the plant to a nearby highway. The map below shows the center of each town, the river, and the highway. The grid lines on the map are 1 mile apart. The cost of the pipeline to Eastville will be $15,000 per mile. The cost of installing pipelines to each of Appalachee and Hull will be $40,000 per mile, since they must go through heavily wooded areas. The cost of building the road will be $180,000 per mile. Assume that the supply pipelines extend to the centers of the three towns and ignore the width of the river. Find the point on the river where the new water treatment plant should be located in order to minimize the total cost of installing the supply pipelines and building the road. Hint:_Decide where (0,0) should be, pick two convenient points on the 'river' and nd the equation of the river-line as a function of x miles. Use the distance formula to find out how far is each town and the highway to the optimal point (x,y). Create the costfunctian and find its minimum. \\