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

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) (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 =
:
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

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

RELATED QUESTIONS
we want to build a 600square metre rectangular enclosure, three sides of which will be... (answered by scott8148)

a dog trainer has 80 feet of fencing with which to create a rectangular area for dogs. if (answered by JulietG)

I would really appreciate a response on this: Jesse wants to build a rectangular... (answered by ikleyn)

A farmer wants to enclose a rectangular field with 180m of fencing. The side of the barn... (answered by stanbon)

To make an enclosure for chickens, a rectangular area will be fenced next to a house.... (answered by josmiceli)

a mpumalsnga farmer needs to buils a rectangular enclosure with 50m of fencing on one of... (answered by Boreal)

You have a 500 foot roll of fencing, which is to form three sides of a rectangular... (answered by Fombitz)

a farmer has 500m of fencing to build a rectangular enclosure along a river.No fencing is (answered by RAY100,Alan3354)

Researchers at a university need a 10,000 square meter rectangular plot on which to grow... (answered by ikleyn)