Question

A construction company has adjoined a 5000 ft^2 rectangular enclosure to its office building. Three sides of the enclosure are fenced in. The side of the building adjacent to the enclosure is 500 ft long and a portion of this side is used as the fourth side of the enclosure. Let x and y be the dimensions of the enclosure, where x is measured parallel to the building, and let L be the length of fencing required for those dimensions.

(a) Find a formula for L in terms of x and y.
L(x,y)=
b) Find a formula that expresses L as a function of x alone.
L(x)=
(c) What is the domain of the function in part (b)? Express as an interval.

Domain =

Answer 1

$\text{The length of the fence is the perimeter of the rectangle minus the common side}$

$\text{with the office building}$

$a) L(x,y) =2*(x+y)-x = 2y+x$

$b) S =x*y; y = \frac{S}{x}= \frac{5000}{x}$

$L(x) = \frac{1000}{x}+x$

$c) \text{Since the length is positive and the side parallel to the building and the office}$

$\text{ cannot exceed 500 ft}$

$\text{Domain} =(0,500]$

Answer: $L(x,y) = 2y+x$ ; $L(x) = \frac{1000}{x}+x$ ;$\text{Domain} =(0,500]$