A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 567567 cubic feet. The concrete for the base costs $22 per square foot, the material for the roof costs $55 per square foot, and the material for the sides costs $4.504.50 per square foot. Find the dimensions of the most economical shed.

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

so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse