algebra word problem

[afrazer721]

Suppose that a livestock rancher wants to enclose a rectangular feedlot on his property. One side of the lot lies along a river and doesn't need to be fenced. The other three sides require fencing. He needs an area of 87,500 square feet to accommodate all of his cattle, and he has 950 feet of fencing. What dimensions should the lot be in order to use as much of the river front as possible?(hint:area of rectangle=length*width).

Area = xy=87.000 square feet
Because no fencing is required against the river, total perimeter of fence is y+x+y=950 ft
Thus, x=950-2y
I plug this into the formula for area and get Area=xy=(950-2y)y
Now I have a function of one variable, 87,500=950y-2y^2
Convert to standard form: 2y^2-950y+87,500=0 and solve for y and get y=125ft wide
Now total length of fence is 125+x+125=950
Solve for x and get x=700ft long
Thus, dimensions are 700ft long by 125ft wide.

If the problem stated what dimensions will maximize the area of the fence, then get into optimization and the second derivative test for curve concaves down (for maximum) or concave up (for minimum).

 

[Deleted member 4993]

Suppose that a livestock rancher wants to enclose a rectangular feedlot on his property. One side of the lot lies along a river and doesn't need to be fenced. The other three sides require fencing. He needs an area of 87,500 square feet to accommodate all of his cattle, and he has 950 feet of fencing. What dimensions should the lot be in order to use as much of the river front as possible?(hint:area of rectangle=length*width). Work out steps to answer, please.

see:

http://www.freemathhelp.com/forum/threads/74063-algebra-word-problem