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?
:
Interesting problem
:
Area:
L * W = 600
L = {{{600/W}}}
:
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( 300, 200, -10, 50, -1000, 5000, 45x+18000/x) }}}
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