A rectangular box with a volume of 1088 ftcubed is to be constructed with a square base and top. The cost per square foot for the bottom is 15cents​, for the top is 10cents​, and for the sides is 2.5cents. What dimensions will minimize the​ cost?What are the dimensions of the box?A. The length of one side of the base is ____ ft?B. The hieght of the box is ____ft?

Answer: x  = 11,09 ft h  =  8,85  ftStep-by-step explanation:Box with square base and topLet  x b a side of the squareA₁  (area of base)     A₁ =  x² area of the top is equal to area of base   A₂  = x²Cost of area A₁    C₁  =  15 * x²Cost of area  A₂C₂  = 10 * x²Area of the side of height  hA₃ =  2*π*x*h                           V = 1088  = x²*h        h  = 1088/x²A₃  = 2*π*x* (1088)/x²     A₃  =   6832,64/xCost  of A₃C₃  = 2,5*4 *6832,64/x           C₃  = 68326,4/xTotal cost CC(x)  = 15x²  +  10x²  +  68326,4/xTaking derivatives on both sides of the equationC´(x)   =  30 x  + 20 x  -   68326,4/x²C´(x)   =  50 x  - 68326,4 /x²        C´(x)   = 0 50 x  - 68326,4 /x²   = 050x³    =   68326,4 x³   =   1366,53 x  = 11,09 ft     and the  height     h  =  1088/x²h  =  8,85  ft