Farmer Ed has 550 meters of fencing, and wants to enclose a rectangular 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?

Question

campbell_st · Answer

ok... so draw a diagram and label the sides

|dw:1411974157511:dw|

the diagram shows the perimeter is 550 metres

the area is 

$$A = x(550 - 2x)$$

or 

$$A = 550x - 2x^2$$

now find the 1st derivative 

$$\frac{dA}{dx}$$

then let it equal zero and solve for x. 

This will be the value that gives the maximum area. 

just work out the dimensions and find the area. 

hope it helps