Answer:
length of the base = 9 ft
and height of the shed = 7 ft
Step-by-step explanation:
given data
volume = 567 cubic feet
base costs = $2 per square foot
roof costs = $5 per square foot
sides costs $4.50 per square foot
solution
we take here length of the base = x ft
and height of the shed = y ft
so Volume will be express as
volume = x²× y
567 = x² × y
y =
and
we know cost of material is express as here
cost of material = cost of base + cost top + cost 4 side ..................1
put here value
cost = x²(2) + x²(5) + 4xy (4.5)
cost = 7x² + 18xy
put here y value
cost = 7x² + 18 x ( )
differentiate and we get
C' = 14x -
we put here C' = 0 and we get
14x - = 0
solve it we get
x = 9 ft
and
y =
y = 7 ft