supposed to solve using optimization.

Problem Overview: The state of Colorado has hired a construction company to build a road that connects two points that are on opposite sides of a mountain. The points are at equal elevations, and an aerial view of the mountain looks like a circle with a radius of 1,000 feet. The options for the route are: - build a road that goes all the way around the mountain, - dig a tunnel straight through the mountain, or - a mix of the two, i.e. build a road part of the way around the mountain and then complete the route with a tunnel straight to the completion point. The construction company will charge about $1,000 per foot for a road that goes around the mountain and a about $2,100 per foot for a tunnel. Your Task: You may work in a group of up to 3 students to complete the following: 1. Use calculus to determine - the best path for the road to take from the construction company's point of view, and - the best path for the road to take from the state's point of view. 2. Determine the total cost for each path. 3. Present your findings in a clear, grammatically correct report, complete with helpful figures that are appropriately labeled