Yes this question in inspired by Jurassic Park.
Basically if you keep feeding goats to a dinosaur you're gonna run out of goats, so I was wondering how many goats are needed (assuming the population is healthy and well fed) such that they can maintain a stable population through breeding while having enough "excess" to keep the Tyrannosaurus happy?
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If Kleiber's law holds true, then Metabolic rate is proportional to M^(3/4)
70 * w^(3/4) = Kilocalorie requirements per day, where w is weight in kilograms.
T-Rex is thought to have weighed between 4500 and 8000 kg. We'll look at the upper end.
70 * 8000^(3/4) = 59,212.790752671590693962072001602
We'll call it at around 59000 food calories per day.
Goat meat has around 1000 to 1400 calories per kg.
59000 / 1000 = 59 kg of goat meat.
Yields for a goat are around 30% to 40% of live weight. Assuming around 70 kg average weight, that's 21kg to 28kg of meat per goat. So 3 goats ought to do it, per day.
Now there will be calories in bone marrow, brain tissue, blood, etc..., but there you go.
T. rex is estimated to have needed at least 200-250 kg of meat daily. An adult goat weighs between 60-90 kg, so each tyrannosaur needs 2-3 goats daily.
Goats produce between 1-3 kids per gestation; on a 5-month cycle a doe can produce 2-3 kids per year. So you’d need a breeding herd of 365 does per dinosaur.
Probably at most half of the weight of a goat is edible meat, so I think you have to at least double your estimate. In addition to that, your herd needs to include some males to fertilize the females (short term one male would suffice and might be very happy, but long term you need more to avoid inbreeding problems and serious genetic diseases), plus some females that have not yet reached reproductive age (as you will have to keep producing new breeding females to replace the ones that get fed to the T-rex).
Something that big ain’t gonna have trouble waiting the goat bones and all and bone marrow is nutritious so I’d imagine bones are to
https://www.researchgate.net/publication/11454500_A_Common_Rule_for_the_Scaling_of_Carnivore_Density
A 9,000kg t rex would need 100*10,000kg of goats. That's 14,285 goats weighing 70kg each.
That is one big pile of goats