Problem 700

12.17 Let $x$ and $y$ (Fig. 12.2) (linear dimensions of the plot in meters), then the area of the plot is $x y=294$, from which $y=\frac{294}{x}$. The length of the entire fence

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Fig. 12.2 can be expressed by the function

$$f(x)=3 x+2 y=3 x+\frac{588}{x}=\frac{3 x^{2}+588}{x}$$

where, by the context of the problem, $x>0$. Further, we have $f^{\prime}(x)=\frac{3 x^{2}-588}{x^{2}}$, from which $\quad f^{\prime}(x)=0 \quad$ when $\quad x=14$ (since $x>0$). If $014$, then $f^{\prime}(x)>0$; therefore, $x=14$ is a point of minimum of the function $f(x)$. As a result, we get $x=14$, $y=21$.

Answer: 14 and 21 m.