'We produce many cheese' is one of the accepted answers. As a native speaker that sounds totally wrong.
Out of curiosity I tried "..much cheese" as well. Also correct.
Can this also be "We produce too much cheese"?
Yes, depending on the context.
Would be along the lines of "nós produzimos queijo demais ."
Not the same as "we produce much cheese"?!?
Thanks. I somehow felt it was!!
"Produced" marked as incorrect, for some reason.
“Produced” still incorrect, Jan 2020.
produced is past
"produzimos" is both present and past tenses.