if you create a calculated dimension like above, and you select a dimension value in this chart, there should be automatically a selection in field PROD_DESC as well as in PROD_CODE.
What Ruben suggests should also work.
Or do the users select in a list box with field PROD_DESC? Then I don't understand why this selection does not limit the values of PROD_CODE as seen in the pivot chart also in other sheets.
What expressions do you use?
Could you upload a small sample that demonstrates that this is not working as expected?