Missing JAVA_VENDOR and JAVA_HOME in WebLogic silent installation

in $DOMAIN_HOME/bin/SetDomainEnv.sh I keep finding:

BEA_JAVA_HOME=""
export BEA_JAVA_HOME

SUN_JAVA_HOME=""
export SUN_JAVA_HOME

if [ "${JAVA_VENDOR}" = "Oracle" ] ; then

(and JAVA_VENDOR is not declared, and *_JAVA_HOME is blank... so WLS fails when started complaining about missing JAVA_HOME....)

The secret is that you should declare (export) these 2 environment variables BEFORE you run the weblogic installation:

export JAVA_VENDOR=Sun
export JAVA_HOME=/usr/java/jdk1.7.0_55/
java -d64 -Xmx1024m -Djava.io.tmpdir=/opt/oracle/temp -jar /software/wls1036_generic.jar -mode=silent -silent_xml=/software/weblogic_silent_install.xml

Why those 2 values cannot be part of the silent installer xml, no clue!

Here is the official doc of the silent installer http://docs.oracle.com/cd/E15523_01/doc.1111/e14142/appendix.htm#WLSIG185