Farmer ed has 400 meters of fencing and wants to enclose a rectangular plot that borders on the river. if farmer ed does not fence the side along the river . find the length and the width of the plot that will maximize the area. what is the largest area that can be enclosed.

112812.5

Step-by-step explanation:

Area = length x width ---> A = L w

Perimeter = 2 * length + 2 * width

BUT ONE of those length measures is NOT needed because of the RIVER.

He does not use the fence along the side of the river

So the formula for THIS particular problem is Perimeter = Length + 2* width  ---> P = L + 2w

Perimeter is 950.

So 950 = L + 2w  > L = 950 - 2w

Plugs this into the area formula.

Area A(w) = L*w = (950 - 2w)*w

This is a parabola (quadratic) function whose max or min

occur at the AVERAGE of the Solutions.

Solving (950 - 2w)*w = 0  

  950 - 2w = 0  OR w=0

 950 = 2w

 w = 475      or w=0

 So the two solutions are zer0 and 475.

 The average of them is (475+0)/2 = 475/2 = 237.5

So the max area is at w=237.5

The Length is then L=950 - 2*237.5 = 950 - 475 = 475

The dimensions that maximize the area are Length L=475 and width w=237.5

The max area is 475 * 237.5 = 112812.5

77

step-by-step explanation: