The largest area that can be enclosed to the nearest square meter will be 348613 m²
<u><em>Explanation</em></u>
Suppose, the length and width of the rectangular plot are
and
respectively.
The farmer does not fence the side along the highway. Lets assume, the <u>farmer does not fence across one length side</u>. So, the total fence needed 
Given that, the length of the fence is 1670 meters. So, the equation will be.....

Now, the area of the plot.....

Taking derivative on both sides of the above equation in respect of
, we will get.....

<u>Now
will be maximum when
</u>. So....

Thus, the area will be: 
So, the largest area that can be enclosed to the nearest square meter will be 348613 m²