Question

Suppose you are designing a cardboard box that must have a volume of cubic feet. The cost of the cardboard is ​$ per square foot. What is the most economical design for the box​ (one that minimizes the​ cost), and how much will the material in each box​ cost?

Answer 1

hello your question lacks some information below is the complete question

Suppose you are designing a cardboard box that must have a volume of 27 cubic feet. The cost of the cardboard is ​$0.15 per square foot. What is the most economical design for the box​ (one that minimizes the​ cost), and how much will the material in each box​ cost?

Answer : Box design , $8.1 ( cost of material in each box)

Explanation:

Volume of cardboard box = 27 cubic feet

cost of cardboard = $0.15 square feet

i) The most economical design for the box would be Designing a square box because the dimensions of the box would be
`\sqrt[3]{27}` = 3 ft

ii) The cost of the material for each box can be calculated as

= surfaces * surface area * cost per square foot

= 6 * 3^2 * $0.15

= $8.1