A farmer prepares his land for plantation during the rainy season. He has right-angled triangle shaped land with length (b) and width (w). Since his land is close to a forest, forest animals sometimes damage his crops. To ward off the animals, he plans to construct an electric fence around his land. He has 120 meters of barbed wire. He wants to cultivate at least 500 square meters of his land. Workers charge €3 to construct a one-meter fence. The farmer is expecting a revenue of €12 per square meter area cultivated. The farmer wants to maximize his profit.
a. Formulate a nonlinear programming model to this problem.
b. Solve the problem using a computer.