Quadratic eqns: farmers fences area, using barn for 1 side

[bottomsup2526]

A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the max area that the farmer can enclose with 80ft of fence? What should the dimensions be to the given area?

1. The max area that the farmer can enclose with 80ft of fence __________ sq. ft.
2. The dimensions of the garden to give this area is 40ft by ___________ ft.

 

[arthur ohlsten]

Re: Quadratic equations, word problem

1)
let 2 sides be x
1 side be y
1 side is barn

2x+y=80
area= xy but y=80-2x
area= x[80-2x]
area= 80x-2x^2
take derivative with respect to x] and set to zero
d[area] / dx= 80-4x
0=80-4x
4x=80
x=20 ft
2x=40 ft
y= 40 ft

area= 800 sq ft
size is 40 ft by 20 ft

Arthur

 

[bottomsup2526]

Re: Quadratic equations, word problem

Thank you so much!! That problem has had me stumped for the last 5 hours.

 

[arthur ohlsten]

Re: Quadratic equations, word problem

you are welcome
Arthur