Description

This challenge is about finding minimums/maximums. The challenge consists of two similar word problems where you will be asked to maximize/minimize a target value.

To make this more of a programming challenge rather than using programming as a calculator, I encourage you to try to find a generic minimize/maximize function rather than just calculating the answer directly.

Challenge

1. A piece of wire 100 cm in length is bent into the shape of a sector of a circle. Find the angle of the sector that maximizes the area A of the sector.

1. A and B are towns 20km and 30km from a straight stretch of river 100km long. Water is pumped from a point P on the river by pipelines to both towns. Where should P be located to minimize the total length of pipe AP + PB?

Challenge Outputs

The accuracy of these answers will depending how much precision you use when calculating them.

1. ~40
2. ~90

Credit

This challenge was adapted from The First 25 Years of the Superbrain. If you have an idea for a challenge please share it on /r/dailyprogrammer_ideas and there's a good chance we'll use it.

Reference Reading (Hints)

https://en.wikipedia.org/wiki/Golden-section_search