SOLUTION: We want to build a 600 square metre rectangular enclosure, three sides of which will be built of wooden fencing at a cost of $15 per metre. The remaining side will be made of cem

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Question 273573: We want to build a 600 square metre rectangular enclosure, three sides of which
will be built of wooden fencing at a cost of $15 per metre. The remaining side
will be made of cement blocks at $30 per metre. How will we set the dimensions
of the enclosure in order to minimize the cost of materials?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
We want to build a 600 square metre rectangular enclosure,
three sides of which
will be built of wooden fencing at a cost of $15 per metre.
The remaining side will be made of cement blocks at $30 per metre.
How will we set the dimensions of the enclosure in order to minimize the cost of materials?
:
Interesting problem
:
Area:
L * W = 600
L = 600%2FW
:
The wooden fencing cost
15(2L + W)
:
The cement block cost
30W
:
Total cost
C = 15(2L + W) + 30W
C = 30L + 15W + 30w
C = 30L + 45W
Replace L with 600/W
C = 30(600/W) + 45W
:
C = 45W + 18000/W
Graph this equation
+graph%28+300%2C+200%2C+-10%2C+50%2C+-1000%2C+5000%2C+45x%2B18000%2Fx%29+
Cost is the vertical y axis and width is the x
Minimum cost occurs when x = 20
So we can say, Make the width 20 meters and the Length 30 meters (30*20=600)
:
What is the min cost:
15(2(30) + 20) + 30(20) =
15(80) + 600 = $18,000
:
:
You can prove this to yourself. Try other dimensions like L=25 W=24 (nearly a square)
15(50 + 24) + 30(24) = $1830, slightly more