1.一楼有文抄公之嫌.先简要回答如下：
1）如果not only...but also...连接的是一个句子之中的并列成分,则无须倒装.
至于具体例句,请参考一楼.
2）但是如果not only...but also...连接的是两个并列的句子,则要求前句采用部分倒装,后句无须倒装.
楼主所给的例句即是用not only...but also...连接两个并列句：food production is important和taking care of the environment (is important),其中后句采用了省略语法.
2.至于部分倒装怎么倒的问题,楼主的关于陈述句变一般疑问句的知识不知道掌握重复否?
部分倒装就等同于对该句进行一般疑问句的变化,即把该句所含的be动词/助动词/情态动词提前.
如：not only (food production is important)
变化成：not only (is food production important)
再如：not only (I can play soccer)
变化成：not only (can I play soccer)
最后如：not only (he likes sports)
变化成：not only (does he like sports)
3.此例句必须倒装,原因在于英语语法的规定是这样的：
如果某句把否定词或含有否定词的短语（包括not only）提前至句首时,则该句必须采用部分倒装.
再如：I have never been to Beijing.
= Never have I been to Beijing.
4.最后,需要提醒楼主的是：如果not only没有提前至句首或not only...but also...不引导并列句时,则不必倒装.
即该例句可以直接写为：
Not only (is food production important) but also taking care of the environment.
= Not only food porduction but also taking care of the environment is important.
5.补充：这题之所以可以不倒装,是因为这是一种不太正式的说法,即：
Not only food production is important but also taking care of the environment.
= Not only food production but also taking care of the environment is important.
因为只是主语的并列,可以不算是句子的并列,所以它可以不用倒装.
也就是说,在不是很正式的情况下,像这样连接两个分句且前一个完整而后一个有省略时,前一句可以不倒装.