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:
[tex]f(p) = -0.0005p^2 + 4p\\\frac{df(p)}{dp}=-0.0010p+4\\-0.0010p+4 =0\\p=4,000[/tex]
The size of the maximum sustainable yield is:
[tex]f(p) = -0.0005p^2 + 4p\\f(4,000) = -0.0005(4,000^2) + 4*4,000\\f(4,000) = 8,000[/tex]
Population = 4,000 hundred metric tons
Size of the yield = 8,000 hundred metric tons
