A fish pond has a carrying capacity $K = 10\,000$ kg of fish. The current stock is $N_{0}=4\,000$ kg and the population follows the logistic growth model $\frac{dN}{dt}= rN\left(1-\frac{N}{K}\right)$ with intrinsic growth rate $r = 0.3$ month$^{-1}$. The farmer harvests a constant amount $H$ (kg per month).

(a) Determine the maximum sustainable harvest $H_{\max}$ (the largest $H$ that can be removed each month without causing the stock to decline).

(b) If the market price of fish is ₦250 per kg and the cost of harvesting is ₦80 per kg, calculate the monthly profit when the farmer harvests $H_{\max}$.

Question

A fish pond has a carrying capacity $K = 10\,000$ kg of fish. The current stock is $N_{0}=4\,000$ kg and the population follows the logistic growth model $\frac{dN}{dt}= rN\left(1-\frac{N}{K}\right)$ with intrinsic growth rate $r = 0.3$ month$^{-1}$. The farmer harvests a constant amount $H$ (kg per month).

(a) Determine the maximum sustainable harvest $H_{\max}$ (the largest $H$ that can be removed each month without causing the stock to decline).

(b) If the market price of fish is ₦250 per kg and the cost of harvesting is ₦80 per kg, calculate the monthly profit when the farmer harvests $H_{\max}$.

Accepted Answer

H_max = 750 kg/month; profit = ₦127,500 per month

Neco 2018 Agricultural Science Question 48

Answer Options

About This Question

Master the Exam!