Yes E is correct.
There are 2 distinct requirements of high-yielding varieties . "Irrigation" and "application of commercial fertilizer". As long as you can clearly identify both, you will not have any trouble choosing the correct answer.
A) requirements of irrigation and application of commercial fertilizer by earlier high-yielding varieties
- looks like commercial fertilizer was applied by high-yielding varieties.
B.requirements by earlier high-yielding varieties of application of commercial fertilizer and irrigation
- makes no sense... application of irrigation...
C.requirements for application of commercial fertilizer and irrigation of earlier high-yielding varieties
- same as B, here only irrigation was required by earlier high-yielding varieties .
D. application of commercial fertilizer and irrigation that was required by earlier high-yielding varieties
- same as C, restrictive clause only modifying irrigation....
E. irrigation and application of commercial fertilizer that were required by earlier high-yielding varieties
- good, 2 seperate requirements.