Farmer Ed has 350 meters of fencing and wants to enclose a rectangle mat plot that borders on a river. If farmer Ed does not fence the side along the river find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed

The length of 175 meters and width of 87.5 meters will maximize the area.

15312.5 square meters.

Step-by-step explanation:  

Please find the attachment.

We have been given that Farmer Ed has 350 meters of fencing and wants to enclose a rectangle mat plot that borders on a river. Farmer Ed does not fence the side along the river.  

First of all we will make a relevant graph to represent the perimeter of fencing for 3 sides as shown in the attachment.

Since Ed will not fence the side along the river, so fencing is needed for 3 sides and perimeter of the fencing would be .

Now we will equate perimeter with 350 as:

We know that area of the rectangle is width times length.

Upon substituting the value of y in area equation, we will get:

Now we will find derivative of area function as:

Now we will equate derivative with 0 and solve for x as:

Upon substituting in equation , we will get:

Therefore, the length of 175 meters and width of 87.5 meters will maximize the area.

Upon substituting in area function, we will get:

Therefore, the largest possible area enclosed would be 15312.5 square meters.

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step-by-step explanation: