Answer:
Length of cheaper side = x = 29.21 ft
Length of expensive side = y = 24.31 ft
Step-by-step explanation:
Let
Length of cheaper side = x
Length of expensive side = y
Total Cost = 5(x + x) + 6(y+y) =
Total Cost = 5(2x) + 6(2y)
Total Cost = 10x + 12y
we also know that
xy = 710ft square
so
y = 710 ft sq. / x
Putting this in total cost equation
Total Cost = 10x + 12( 710 ft sq. / x )
f(x) = 10x + ( 8,520 ft sq. / x ) ( cost = f(x)
f'(x) = 10 - ( 8,520 ft / x^2 ) (x>0)
0 + ( 8,520 ft / x^2 ) = 10
8,520 ft / x^2 = 10
x^2 = 8,520 ft / 10
(x^2)^1/2 = (8,520 ft / 10)^1/2
x = 92.3 / 3.16
x = 29.21 ft
As given
xy = 710ft square
Putting value of x in above equation
29.21 y = 710
y = 710/29.21
y = 24.31 ft
