bash shell mkdir{x..y} with variables

Question

I am trying to create directories 1-15 in single line mkdir with a script.
The complete working command is: mkdir testdir{1..15}
This command create 15 directories: testdir1, testdir2, testdir3..

I defined: Directory name, range-start and range-end as variables.
Instead of getting 15 directories on the given path (testdir1, testdir2, ..) I get 1 directory named:
testdir{1..15}

What am I doing wrong ?

#!/bin/bash

path=/export/lofi
range_start=1
range_end=15
dirname=testdir
cd "$path"
echo "Current directory: `pwd`"
echo "Creating directories from $range_start - $range_end"
mkdir $dirname{$range_start..$range_end}
echo $dirname{$range_start..$range_end}

I tried:

mkdir $dirname{$range_start..$range_end}
mkdir '$dirname{$range_start..$range_end}'
mkdir $dirname`{`$range_start..$range_end`}`
mkdir "$dirname{$range_start..$range_end}"