Answer:
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
