An Open Box Is to Be Constructed from a Piece $15$

question 30

Essay

An open box is to be constructed from a piece of sheet metal $15$ in by $25$ in by cutting squares of length $x$ from each corner and folding up the sides.
(a) Express the volume $V$ of the box as a function of
$x$ .
(b) What is the domain of $V$ ?
(c) Draw a graph of the function $V$ and use it to estimate the maximum volume for the box.

---

Definitions:

Pull Strategy

A marketing strategy designed to create demand for products directly from consumers, leading retailers to stock the product due to increased consumer demand.

Retailers

Businesses that sell goods or services directly to consumers, often in small quantities.

Push Strategy

A marketing strategy focused on pushing products through the distribution channels to the end consumers by promoting goods to wholesalers, retailers, or directly to consumers.

Purchase Stage

A phase in the buying process that involves the actual acquisition of a product or service by a consumer or organization.