A landscape architect wished to enclose a rectangular garden

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $50/m and on the other three sides by a metal fence costing $10/m. If the area of the garden is 108 square meters, find the dimensions of the garden that minimize the cost.

xy=108, with x,y lenghts of sides.

And we minimize 50x+10x+2(10y)=60x+20y.

So, substitute x=108/y,

so 60x+20y=(108*60/y)+20y.

Now differinate and set to 0.
So, -(108*60/y^2)+20=0, or 20=(108*60)/y^2.

So, y=sqrt((108*60)/20) =324.

So, lenght of side with bricks is 108/(sqrt324) = 6
And adjacent side is 324 = 18

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $50/m and on the other three sides by a metal fence costing $10

A landscape architect wished to enclose a rectangular garden

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