Assignment 2 Optimization Problems 1. The cost of pipe to go underwater is 60% more than the cost of pipe used in dry-land situations. A pipeline must be extended from point A to refinery B, 8 km down the river. The river width is 1 km. Find the best way to cross the river so u that the total cost of the pipe is the lowest one. {2K, 4A, 2C) 2. An isosceles triangle is inscribed in a circle the radius of which is 10 cm. a. Find all angles ofthe triangle, maximizing the area of the triangle. b. Determine the maximum area of the triangle. (2K, 4T, 2C) 3. Determine the shortest distance from point A (3, 0) to the parabola y = x2. (2K, 4T, 2C} If AB is the shortest line segment from the point A to the parabola, find the angle between AB and the tangent to the parabola at the point B. (2K, 4A, 2C) River