# Animations with Reveal.js and SVG.js

Created by Asvin Goel

# Monty hall problem

## Branch and bound

Solution: $(x,y) = (3.8,3)$ Branch $x \geq 4$ Branch $x \geq 4$ ⟶ $(x,y) = (4,2.9)$ Branch $x \geq 4$, $y \geq 3$ Branch $x \geq 4$, $y \geq 3$ ⟶ infeasible Discard branch: $x \geq 4$, $y \geq 3$ Branch $x \geq 4$, $y \leq 2$ Branch $x \geq 4$, $y \leq 2$ ⟶ $(x,y) = (4,2)$ $(x,y) = (4,2)$ is an integer solution Branch $x \leq 3$ Branch $x \leq 3$ ⟶ $(x,y) = (3,2.6)$ Branch $x \leq 3$, $y \geq 3$ Branch $x \leq 3$, $y \geq 3$ ⟶ infeasible Discard branch: $x \leq 3$, $y \geq 3$ Branch $x \leq 3$, $y \leq 2$ Branch $x \leq 3$, $y \leq 2$ ⟶ $(x,y) = (1.8,2)$ Branch $x \leq 3$, $y \leq 2$, $x \geq 2$ Branch $x \leq 3$, $y \leq 2$, $x \geq 2$⟶ $(x,y) = (2,2)$ $(x,y) = (2,2)$ is an integer solution Branch $x \leq 3$, $y \geq 3$, $x \leq 1$ Branch $x \leq 3$, $y \geq 3$, $x \leq 1$ ⟶ $(x,y) = (1,1.6)$ $(x,y) = (1,1.6)$ is worse than best integer solution All branches solved, $(x,y) = (2,2)$ is optimal

## Big-M constraint

$y \leq 1 + M(1-z)$ with $z=1$

## Big-M constraint

$y \leq 1 + M(1-z)$ with $z=0$ and sufficiently large $M$

## The end

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