SOLUTION: A rectangular area is to be fenced in using two types of fencing. The front and back uses fencing costing RM 5 a foot while sides use fencing costing RM 4 a foot. If the area of t

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Question 1036851: A rectangular area is to be fenced in using two types of fencing. The front and back uses fencing costing RM 5 a foot while sides use fencing costing RM 4 a foot. If the area of the rectangle must contain 500 square feet, what should the dimensions of the rectangle be in order to keep the cost at a minimum ?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular area is to be fenced in using two types of fencing.
The front and back uses fencing costing RM 5 a foot while sides use fencing costing RM 4 a foot.
If the area of the rectangle must contain 500 square feet, what should the dimensions of the rectangle be in order to keep the cost at a minimum ?
:
let L = the length of the area
let w = the width
Area
L * w = 500
L = 500%2Fw
:
Cost of fencing
Cost = 5(2L) + 4(2W)
C = 10L + 8w
Replace L with 500/w
C = 10(500%2Fw + 8w
graph this equation :y = 5000%2Fw + 8w
+graph%28+300%2C+200%2C+-10%2C+60%2C+-100%2C+600%2C+%285000%2Fx%29%2B8x%29+
Cost is on the y axis, width on the x axis
w = 25 ft for min cost
then
L = 500/25; minimum cost would calculate to: $400
L = 20 ft is length