1. The problem statement, all variables and given/known data You're building a walkway from the corner of one building to the corner of another building. The diagram looks like this. The street is 100 ft wide, and 50 ft long. The walkway will weigh 40 pounds per feet when it is parallel to the street and 30 pounds per feet when it is crossing the street. How should the walkway be laid out to have a minimal weight? 2. Relevant equations I'm going to call the horizontal portion of the walkway x ft of length, and the portion that crosses the street y ft of length. So the total length of the walkway would be x+y. Then the equation for the total weight of the walkway would be 40x + 30y, right? Also I'm not sure if the pythagorean theorem should come into play here. 3. The attempt at a solution This is where I'm really, really confused. I know that when you do an optimization problem , the hard part is finding the right equation. I have no idea what that is. Can someone just give me a little prod in the right direction? Thanks.