Shell script is not writing to log file

[linuxxphybrid]

I have the following shell script.

#!/bin/bash
# Variables
LOGFILE="/home/admin/cron/http_log"

# redirect STDOUT stream to LOGFILE
exec 1>>$LOGFILE

echo "GET /" | nc localhost 80

(The file name is /home/admin/cron/checkhttp.sh and the directory /home/admin/cron/, its subdirectories and all files in the directory and subdirectories have

Owner root
Group psaadm

and the file's permission is set to rxwr-xr-x. I set up a cron job in Plesk so that the script is executed every 5 minutes; its configuration is as follows:

Min */5
H *
DM *
M *
DW *
Command /home/admin/cron/checkhttp.sh)

The script is not writing to /home/admin/cron/http_log, and I don't know why. Why is the script not writing to /home/admin/cron/http_log? How can I fix the problem?