Optimization Calculus
posted by Nicole
A three sided fence is to be built next to a straight section of river, which forms the fourth side of a rectangular region. There is 96 ft of fencing available. Find the maximum enclosed area and the dimensions of the corresponding enclosure.
I drew a picture of it and I got the area = x*y. I used x as the two widths and y as the length on the picture.

Steve
so, now go for it. You know that
2x+y = 96, so y = 962x
the area is xy = 2x(962x) = 192x  4x^2
That's just a parabola; its vertex gives the maximal area. 
Bianca
since there are usually four sides to a square(which is the optimal shape), you would do 96/4 to figure out what one side would be. Then since one side is missing, you'd add that one side to the other side. So s= side, 2s to find the other side length, which would then be 48. So the dimensions would just be, 24 by 24 by 48 to get the maximum area.
Respond to this Question
Similar Questions

Calculus
A threesided fence is to be built next to a straight section of a river, which forms the fourth side of a rectangular region. The enclosed area is to equal 3200 m2. What is the minimum perimeter that such a fence can have? 
precalc
area of a rectangular region: a farmer wishes to create two rectangular regions bordering a river, by three fences perpendicular to the river and one connecting them. suppose that x represents the length of each of the three parallel … 
CalculusApplied Optimization Quiz Problem
A rancher wants to fence in a rectangular area of 23000 square feet in a field and then divide the region in half with a fence down the middle parallel to one side. What is the smallest length of fencing that will be required to do … 
Calculus  Optimization
A fence is to be built to enclose a rectangular area of 800 square feet. The fence along 3 sides is to be made of material $4 per foot. The material for the fourth side costs $12 per foot. Find the dimensions of the rectangle that … 
college Algebra
A rectangular fence is to be built along a river using the river as one side of the fence.the cost of the fencing for the two ends is $8 per sq ft and the cost of the fencing for the side running parallel to the river is $12 per sq … 
problem solving
What about regions built along a natural boundary? 
Precalculus
A farmer has 1000 feet of fencing materials available to fence a rectangular pasture next to a river. If the side along the river does not need to be fenced, what dimensions maximize the enclosed area? 
Math
1. A threesided fence is to be built next to a straight section of river, which forms the fourth side of a rectangular region. The enclosed area is to equal 1800 ft2. Find the minimum perimeter and the dimensions of the corresponding … 
AP Calculus AB
The fence around Wayne Manor (a rectangular plot of land) is going to be replaced. No fence will be required for the side lying along Gotham river. If the new wrought iron fence costs $12 per meter for the side parallel to the river … 
DerivativeOptimization Problems
You plan to enclosed part of a rectangular farmland with a fence. Since one side of it is bounded by a river, you only need to fence the other three sides. if you have enough budget to buy 600m of fencing material, what is the largest …