Ajewelry box with a square base is to be built with copper plated sides, nickel plated bottom and top, and a volume of 40cm^3. if nickel plating costs $2 per cm^2 and copper plating costs $1 per cm^2, find the dimensions of the box to minimize the cost of the materials. write out the process of solving this question in plain english

Length and width = 2.71 cm and height = 5.43 cm

Step-by-step explanation:

Let the length of the jewelry box = x

Let the width = x          [box is square, so length and width are same]

Let the height = y

Given volume = 40 cm³

Therefore, V = x²y

x²y = 40  

y =

Cost of Nickle plating on top and bottom = $2 per cm²

Cost of copper plating on sides = $1 per cm²

Cost = 2(Areas of top and bottom) + 1(Areas of sides)

       = 2(x² + x²) + 1(xy + xy + xy + xy)

       = 4x² + 4xy

       = 4x² = 4x

f(x)   = 4x² +  

f'(x)  = 8x -  

f"(x)  =

f'(x)  = 0

x³ = 20

x = ∛20

x  = 2.71 cm

x²y = 40  

∛400y = 40

y =

  =

y  = 5.4288 ≈ 5.43 cm

Length and width = 2.71 cm and height = 5.43 cm

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.