So...

We are trying to find the maximum value of the function \(Y(p)={900p\over2+p}\) within the domain \(x\ge0\). This is the graph of a **hyperbola**, and it is positive. So, in order to find the maximum value of the function, we have to get its **horizontal asymptote**. An asymptote is a line that a graph approaches but never touches. The rules are as follows:

1. If the numerator's degree is less than the denominator's degree, then the horizontal asymptote is **y = 0.**

2. If the numerator's degree is equal to the denominator's degree, the the horizontal asymptote is the quotient of the coefficients of the highest degree terms.

3. If the numerator's degree is greater than the denominator's degree, then it does not have a horizontal asymptote.

The degree of **900p** is 1, and the degree of **2+p** is 1. Therefore, the horizontal asymptote is \(y={900\over1}\), or just \(y=900\). This means that the maximum value of the function is **900**.

What this actually means is that the function approaches 900 as you go farther along the x-axis, or, as you increase the amount of pesticide. So, theoretically, if you had infinite pesticide, you would have 900kg of extra yield. But... infinity is tricky. Just trust me, the answer is 900.