W3 Total Cache Error: Files and directories could not be automatically created t

W3 Total cache throws me the error:

W3 Total Cache Error: Files and directories could not be automatically created to complete the installation.
Please execute commands manually View required changes
or use FTP form to allow W3 Total Cache make it automatically. Update via FTP

I read already couple of articles trying to resolve it but It didn’t succeed.

Here is the configuration that I have:

WordPress: 4.3.1
W3 Total Cache: 0.9.4.1
Apache: 2.2.29 (Unix)
PHP: 5.3.29
Linux (AWS ec2 i386)
Apache user: user1
Apache group: user1

Document Root: /var/www/html/website/blog/wordpress/
Document Root permissions:
drwxr-xr-x 5 user1 user1 4096 Oct 16 08:30 wordpress
Document Root .htaccess permissions:
-rw-r--r-- 1 user1 user1 213 Oct 16 07:41 .htaccess
wp-content permissions:
drwxrwxrwx 8 user1 user1 4096 Oct 16 09:01 wp-content

Vhost :
#My blog is part of a domain name which runs a web app on JAVA and the blog can be accessed at https://mybwesbite.com/blog

...
<Directory /var/www/html/website/blog/wordpress>
Options FollowSymLinks
AllowOverride All
</Directory>

ProxyPass /blog !
Alias /blog /var/www/html/website/blog/wordpress/
....
# info: the blog can be accessed properly and everything is fine

var/www/html/website/blog/wordpress/.htaccess:

<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /blog/
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /blog/index.php [L]
</IfModule>

Additional information – Here is a part of the Code that W3 Total cache tell me to enter the .htaccess

# BEGIN W3TC Page Cache core
...
    RewriteCond "%{DOCUMENT_ROOT}/var/www/html/website/blog/wordpress/wp-content/cache/page_enhanced/%{HTTP_HOST}/%{REQUEST_URI}/_index%{ENV:W3TC_PREVIEW}.html%{ENV:W3TC_ENC}" -f
    RewriteRule .* "/var/www/html/website/blog/wordpress/wp-content/cache/page_enhanced/%{HTTP_HOST}/%{REQUEST_URI}/_index%{ENV:W3TC_PREVIEW}.html%{ENV:W3TC_ENC}" [L]
...
# END W3TC Page Cache core

We can see the in the “RewriteCond” the PATH seems incorrect because I guess it should be instead something like: “%{DOCUMENT_ROOT}/wp-content/cache/page_enhanced/%{HTTP_HOST}/%{REQUEST_URI}/_index%{ENV:W3TC_PREVIEW}.html%{ENV:W3TC_ENC}”

It seems that w3 total cache doesn’t get the proper “DOCUMENT_ROOT”. That’s just my guess.

What else can I do?

https://wordpress.org/plugins/w3-total-cache/