SOLUTION: we want to build a 600square metre rectangular enclosure, three sides of which will be built of wooden fencing at a cost of $14 per metre. the remaining side will be made of cement

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: we want to build a 600square metre rectangular enclosure, three sides of which will be built of wooden fencing at a cost of $14 per metre. the remaining side will be made of cement      Log On


   

Question 332493: we want to build a 600square metre rectangular enclosure, three sides of which will be built of wooden fencing at a cost of $14 per metre. the remaining side will be made of cement blocks at $28 per metre. How will we set the dimensions of the enclosure in order to minimize the cost of materials?
please help.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
if the dimensions are x and y ___ xy = 600 ___ x = 600/y

for the cost ___ C = 14(2y + x) + 28(x) = 28y + 42x

substituting ___ C = 28y + (25200/y)

___ this is calculus ___
at the minimum point of the graph , the slope of the tangent to the curve (1st derivative) is equal to zero

dC/dy = 28 - (25200 / y^2) = 0

28 y^2 = 25200 ___ y = ± sqrt(25200/28) = ± 30 ___ negative value is not realistic

the dimensions are 20 by 30 , with the longer sides being wood (and one of the shorter sides)