Homework SourseA manufacturer manufactures an open trash bin Each bin must
A manufacturer manufactures an open trash bin. Each bin must be 10 feet tall and have a volume of 720 cubic feet. If the material for the front and back costs $7 a square foot, the material for the sides costs $14 a square foot, and the material for the bottom costs $20 a square foot, find the dimensions x and y that minimize the total cost, and the find the total cost.
Solution
let the base dimensions be l , b and height is 10 l= x; b= y amount = bx10x7x2 + lx10x14 + 20x l xb given lxbx10 = 720 lxb= 72 amount = 140(l+b) + 1440 amount is minimum when l= b (Arithmetic mean >= Geometric mean) therfore , l=b= sqrt (72) = 8.49 feet minimal cost = 140(2*8.49) + 1440 = 3817.2 sq.feet
