Problem #PRU-64548

Problems Functions of one variable. Continuity Algebra Algebraic inequalities and systems of inequalities Quadratic inequalites (several variables) Monotonicity, boundedness Calculus

Problem

You are mixing four magic potions, and you choose how much of each one to use. Let \(a\), \(b\), \(c\), and \(d\) be the amounts of the four potions you pour in, each chosen between \(0\) and \(1\) liter. The wizard tells you that the magic power of your mix is given by the formula \[a + b + c + d - ab - bc - cd - da.\] What is the largest magic power you can create?