Suppose that $x$ and $y$ satisfy $$3 x + y = 18 , \quad x \geqq 1 , \quad y \geqq 6 .$$ We are to find the maximum value and the minimum value of $x y$. When we express $x y$ in terms of $x$, we have $$x y = \mathbf { A B } ( x - \mathbf { C } ) ^ { 2 } + \mathbf { D E } .$$ Also, the range of values which $x$ can take is $$\mathbf { F } \leqq x \leqq \mathbf { G } .$$ Hence, the value of $x y$ is maximized at $x = \mathbf { H }$ and its value there is $\mathbf { I J }$, and the value of $x y$ is minimized at $x = \mathbf { K }$ and its value there is $\mathbf { L M }$.
Suppose that $x$ and $y$ satisfy
$$3 x + y = 18 , \quad x \geqq 1 , \quad y \geqq 6 .$$
We are to find the maximum value and the minimum value of $x y$.
When we express $x y$ in terms of $x$, we have
$$x y = \mathbf { A B } ( x - \mathbf { C } ) ^ { 2 } + \mathbf { D E } .$$
Also, the range of values which $x$ can take is
$$\mathbf { F } \leqq x \leqq \mathbf { G } .$$
Hence, the value of $x y$ is maximized at $x = \mathbf { H }$ and its value there is $\mathbf { I J }$, and the value of $x y$ is minimized at $x = \mathbf { K }$ and its value there is $\mathbf { L M }$.