"If all else fails time for ORC MEAT!"
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Yep. "Looks like meat's back on the table, boys!"
(One of the few PJ added/altered lines in the movies that worked).
And if Minas Tirith was under siege they could probably get some supplies in and people out using back paths into and out of the city, rather like the besieged Union Army did at Chattanooga in 1864, before Grant took over. Confederates occupied Missionary Ridge, etc. and blocked river and most, but not all, land passages.