College Algebra
posted by Melanie .
A farmer has 100 yeards of fencing with which to enclose two adjacent rectangular pens both bordering a river. The farmer does not need to fence the side with the river. What should the dimensions of the two pens together (a rectangle) be in order to yield the largest possible area?

Perimeter = 3w+4L=100
area= 2LW
but W=(1004L)/3
area=2L (1004L)/3
take the derivative with respect to L, set to zero, and solve for L, then go back and find W. 
Ooops. You are not a calculus student yet.
area=2L(1004L)/3= 200L/3 8L^2/3
This is a parabola, with zeroes at L=25, and L=0. So max must be halfway between, L=25/2
if L = 25/2 then W=(10050)/3 and that is it. 
Thank you bobpursley!
Respond to this Question
Similar Questions

Math
A farmer with 8000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? 
Calc.
Please help solve this, A farmer has 600m of fence and wants to enclose a rectangular field beside a river. Determine the dimensions of the fence field in which the maximum area is enclosed. (Fencing s required on only three sides: … 
algebra
A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 100 ft. of fence? 
College Math
farmer wishes to fence a rectangular area along the river bank. No fence is required on the side adjacent to the river. The material for the fence costs P16.00 per meter for the side parallel to the river, P12.00 per meter for the … 
Algebra  Math
A farmer has 100 yards of fencing with which to enclose two adjacent rectangular pens  both bordering a river. The farmer does not need to fence the side with the river. What should the dimensions of the two pens Together (rectangle … 
word problem
a farmer has 800 yards of fencing to enclose a rectangular pasture. Since one side of the pasture boarders a river that side does not need to be fenced. if the side perpendicular to the river must be twice as long as the side parallel … 
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 … 
Algebra
Word Problems: 1. A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. If he needs no fence along the river, what are the dimensions of the field that he can fence with the largest … 
algebra
Farmer Ed has 9 comma 0009,000 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, what is the largest area that can be enclosed? 
Algebra
Farmer Ed has 9,000 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, what is the largest area that can be enclosed?