Question

The reproduction function for a sardine is f(p) = −0.0005p2 + 4p, where p and f(p) are in hundred metric tons. Find the population that gives the maximum sustainable yield, and the size of the yield. population hundred metric tons size of the yield hundred metric tons

Answer 1

Answer:

Population (p) = 4,000 hundred metric tons

Size of the yield (f(p)) = 8,000 hundred metric tons

Step-by-step explanation:

The population of sardines 'p', for which the derivate of the function f(p) is zero, is the population that gives the maximum sustainable yield:

$f(p) = -0.0005p^2 + 4p\\\frac{df(p)}{dp}=-0.0010p+4\\-0.0010p+4 =0\\p=4,000$

The size of the maximum sustainable yield is:

$f(p) = -0.0005p^2 + 4p\\f(4,000) = -0.0005(4,000^2) + 4*4,000\\f(4,000) = 8,000$

Population = 4,000 hundred metric tons

Size of the yield = 8,000 hundred metric tons