You need to construct a closed rectangular box with the volu

You need to construct a closed rectangular box with the volume 60 m^3. The material used for the sides will cost $1/m^2, while the material for the bottom will be $3/m^2 and for the top will be $2/m^2. What dimensions will minimize the total cost of the box?

if the box dimensions are lxbxh

=> lbh = 60

and Total Cost = 3lb+2lb+1x(2lb+2bh) = 5lb+2lh+2bh

since AM is always greater than GM

=> (5lb+2lh+2bh)/3 >= (20(lbh)²)^1/3

and to minimize it

5lb = 2lh = 2bh => 2.5l = 2.5b = h

=> 2.5l³ = 60

=> l = 2.8845m => h = 7.21m

So the dimensions are 2.8845 x 2.8845 x 7.21 m

You need to construct a closed rectangular box with the volume 60 m^3. The material used for the sides will cost $1/m^2, while the material for the bottom will

You need to construct a closed rectangular box with the volu

Solution

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