1. Ok with your defininition of x
let the other side (parallel to house) by y
so y + 2x = 40
y = 40-2x
Area = xy = x(40-2x) or
Area = 40x - 2x^2
2. clearly 0<x<20 or else the bracket (40-2) becomes negative.
3.
40x - 2x^2 = 0
2x(20-x) = 0
x = 0 or x = 20
4. you should get a vertex of (10,200)
x=10 , y = 20
A homeowner has forty feet of fencing to enclose three sides of a rectangular patio. The fourth side of the patio is a side of the house, and requires no fencing.
1. Let x represent the side of the rectangle perpendicular to the house (this helps avoid having ½ in the equation) and write an expression for the area as a function of x.
2. Give the domain by examining the equation from number 1.
3. Find the zeros of the equation.
4. Plot the zeros on a graph and find the x-coordinate of the vertex. Find the y-coordinate and make a sketch of the graph on the domain of x.
5. What should be the dimensions of the enclosure in order to maximize the area? What is the maximum area?
2 answers
The management of the UNICO department store has decided to enclose a 940 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $5/running foot and the steel fencing costs $3/running foot, determine the dimensions of the enclosure that can be erected at minimum cost