A Fisheries Problem

Calculus Level 4

A fish farmer wants to use a pond for his fishing. He finds that the pond has a capacity of \(M\) fish.

He also finds that population growth rate is proportional to the product of 'the number of fish in the pond' and 'the additional number of fish which can be accommodated in the pond'; with a proportionality constant \(\alpha\).

If the optimal rate of harvest is \(R\), what is the value of \(\left\lfloor\frac{1000R\pi}{\alpha M^2}\right\rfloor\)

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