please help A storage shed is to be built in the shape of a box with a square ba

Question

please help

A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 729 cubic feet. The concrete for the base costs $3 per square foot the material for the roof costs $2 per square foot and the material for the sides costs $2.50 per square foot. Find the dimensions of the most economical shed. The length of one side of the shed's base is ft. The height of the shed is ft. Find the volume of the largest open box that can be made from a piece of cardboard 17 inches by 10 inches by cutting equal squares from the comers and turning up the sides. The maximum volume is in3. (Round to the nearest hundredth as needed.)

Explanation / Answer

1. let the base length be b and height be h

now volume =b*b*h =729 ;

cost of total shed = 5(b^2) +2.5*b*h which is to be minimized

b^2 =729/h =>b = 27/(h^0.5) ;

so cost = (3645/h) +2.5*(h^0.5)

differentating wrt to h and equating to 0 => -3645/(h^2) +1.25 /h^0.5 =0 =>h = h^2.5 =3645*4/5 => h = 24.317fts;

b = 29.97fts;

2.

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