Optimization

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Two positive numbers have a sum of $s = 40$. Let $x$ be one of the two numbers, so the other is $s - x$. Find the value of $x$ that maximizes the product $x(s - x)$, and give the maximum product.

2. Warm-up

   Two positive numbers have a sum of $s = 78$. Let $x$ be one of the two numbers, so the other is $s - x$. Find the value of $x$ that maximizes the product $x(s - x)$, and give the maximum product.

3. Warm-up

   Two positive numbers have a sum of $s = 26$. Let $x$ be one of the two numbers, so the other is $s - x$. Find the value of $x$ that maximizes the product $x(s - x)$, and give the maximum product.

Problems shown under their original terms: Generated (template, solver-computed).