Posted by angel on Wednesday, April 18, 2012 at 8:44pm.
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 80 feet of fence? What should the dimensions of the garden be to give the area?

word problem  Reiny, Wednesday, April 18, 2012 at 9:44pm
He will need one length and two widths
let the length by y ft
let the width be x ft
2x + y = 80
y = 802x
area = xy
= x(802x)
= 2x^2 + 80x
The x value to produce the maximum area is the x of the vertex of this parabola.
If you know Calculus
d(area)/dx = 4x + 80= 0 for a max of area
x = 20
then y = 802x = 40
the field should be 20 by 40 , with 40 being the one side.
nonCalculus:
the x of the vertex of y = ax^2 + bx +c is b/(2a)
which in this case is 80/(2(2)) = 20
continue as above.
or you can complete the square:
area = 2(x^2  40x + 400  400 )
= 2(x20)^2 + 800
max of area is 800 when x = 20 and y = 40

word problem  gordana, Sunday, September 14, 2014 at 9:47am
The farmer wants to use the 500 m to an enclosure divided into two equal areas. What is the total maximum area that can is achieved with the 500 m fence. use differential calculus to the solution.
Answer This Question
Related Questions
 algebra  A farmer decides to enclose a rectangular garden, using the side of a ...
 Math  A farmer decides to enclose a rectangular garden, using the side of a ...
 algebra  A farmer decides to enclose a rectangular garden, using the side of a ...
 Algbera  Afarmer decides to enclose a rectangular garden, using the side of a ...
 Algebra  A farmer decides to enclose a rectangular garden, using the side of a ...
 Algebra  a farmer wants to enclose a rectangle garden using the sides of her ...
 Math(HELP!)  A farmer has 120 feet of fencing to enclose a rectangular plot for...
 College Algebra  A farmer wants to build a rectangular fence using the side of ...
 math  A farmer will make a rectangular pen with 100 feet of fence using pasrt ...
 calculus optimization problem  A farmer has 460 feet of fencing with which to ...
More Related Questions