A company produces open-top boxes with square bases for metal containers. The base of the boxes is made of different materials than the sides. The box is assembled by riveting a bracket at each of the eight corners. The total cost of producing a box is the sum of the cost of the materials for the box and the labor costs associated with affixing each bracket. As a consultant of the company, you need to devise a formula for the total cost of producing each box and determine the dimensions that allow a box of specified volume to be produced at minimum cost.
Use the following notation to solve this problem.
Volume of the box = V
Height of the box = h
Length of sides of each base = x
Cost of the material for the base = A per square unit
Cost of the material for the sides = B per square unit
Cost of each bracket = C 1.
Write an expression for the company’s total cost in terms of these quantities.
