$2\mathrm{.}8$ algorithm design

Suppose we are given a set of $n$ rectangles, denoted $R_1,$dots,$R_n.$ Each rectan$-$

gle $R_i$ is specified by four integers $b_i,h_i,l_i,w_i$ :

$b_i$ is the $y-$coordinate of the base of $R_i,$

$h_i>0$ is the height of $R_i,$

$l_i$ is the $x-$coordinate of the left side of $R_i,$ and

$w_i>0$ is the width of $R_i.$

We want to find a new rectangle $R$ with the smallest area such that it encloses

all $n$ rectangles $R_i,$dots,$R_n.$ The sides of the rectangle $R$ will be parallel to

the $x-$ and $y-$axes. Design and analyze an algorithm that solves this problem

using at most $3n-4$ comparisons.