an architect wants to enclose a rectangular garden on one side by a brick wall...

R

Ryan

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...costing $12 per foot and on the? A landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $12 per foot and on the other three sides by a metal fence costing $4 per foot. If the area of the garden is 450 ft2, find the n minimizing the cost.dimensions of the garde
 
call x the dimension with the brick, y the other

xy = 450
Cost = C = 12x + 4x + 2*4y = 16x + 8y
substit
C = 16x + 8(450/x)
C = 16x + 3600/x
differentiate to get max/min
C' = 0 = 16 – 3600/x²
multiply by x²
16x² = 3600
x = 15 ft
y = 30 ft

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