A rectangular garden, 800 m^2, is to be surrounded on three sides by a brick wall and on the forth side by a picket fence. The cost of the brick wall is 85/m and the cost of the fence is $17/m. Find the dimensions of the garden that minimize the cost of the fence:
a) 28.3mby 28.3m
b) 20m by 40 m
c) 25 m by 32 m
d) 21.9 m by 36.5m
2007-05-17 06:10:24 · 3 answers · asked by James P 1 in Science & Mathematics ➔ Mathematics
You want to minimize the cost of the brick wall and fence put together, right? Because if you just want to minimize the *fence,* pick b) and put the fence on one of the 20m sides.
But to minimize the entire cost, let's develop equations for each choice. We'll assume that the (cheaper) picket fence is going to be on the short side where applicable.
a) c = 3 * 28.3* 85 + 28.3* 17 = 7697.6
b) c = 2*20*85 + 40*85 + 40*17 = 7480
c) c = 2*25*85 + 32*85 + 32 *17 = 7514
d) c = 2* 21.9* 85 + 36.5 * 85 + 36.5* 17 = 7446
I guess it's d) !
2007-05-17 06:15:50 · answer #1 · answered by Timothy H 4 · 0⤊ 0⤋
The smallest perimeter wil occur when the rectangle is a square. Thus a square will result in the minimum cost.
Thus sqrt (800) = 28.284 m per side is the correct answer.
2007-05-17 13:20:50 · answer #2 · answered by ironduke8159 7 · 0⤊ 2⤋
bit tough 4 me-try ask.com if u want it working`out`www.ask.com
2007-05-17 13:16:45 · answer #3 · answered by Anonymous · 0⤊ 2⤋