Example: 120 farm workers cultivate 50 hectares of land, this

crop name workers required per hectare estimated output value per hectare
\begin{tabular}{lll} 
vegetables & $\frac{1}{2}$ & 11000.00 yuan \\
cotton & $\frac{1}{3}$ & 7500.00 yuan \\
rice & $\frac{1}{4}$ & 6000.00 yuan
\end{tabular}

Question: How should it be arranged so that every hectare of land is planted with crops, all workers are employed, and the total estimated output value of agricultural products is maximized?
Let the land for growing vegetables, cotton, and rice be $x$ hectares, $y$ hectares, and $z$ hectares, respectively, and the expected total output value be $W$ yuan. According to the given conditions, we have
$$
\begin{array}{l}
x+y+z=50, \\
\frac{1}{2} x+\frac{1}{3} y+\frac{1}{4} z=20 . \\
W=11000 x+7500 y+6000 z .
\end{array}
$$

From (1) and (2), we get $y=90-3 x, z=2 x-40$.
Substituting into (3), we get $W=50 x+435000$.
By $x \geqslant 0, y=90-3 x \geqslant 0, z=2 x-40 \geqslant$ 0, we get
$$
20 \leqslant x \leqslant 30 \text {. }
$$
$\therefore$ When $x=30$, $W$ reaches its maximum value of 450000 yuan, at which point $y=0, z=20$.

Thus, planting 30 hectares of vegetables and 20 hectares of rice will maximize the expected total output value, which can reach 450000 yuan.