Math 1050 Project 2
Tuna Fish Project
Applications of Polynomials
Introduction
Often, in manufacturing, decisions must be made that involve optimization:
minimizing costs, minimizing materials waste, maximizing profit, etc. In this
project, you are going to examine the process of maximizing the volume of a
container that is made from a given amount of material.
Part I: Maximizing the volume of an open box
Consider making an open box which is made from a 16" by 48” rectangular piece
of cardboard by cutting equal sized squares from each corner and folding up the
sides. Let x be the side of the squares that are cut out.
1 a) Write the function V which gives the volume of the box as a function of x.
b) What is the 'real world' domain of V?
c) Graph y = V(x) on an appropriate viewing window to get a picture which shows
the turning point and x-intercepts of the function on its real-world domain. Sketch
what you see by appropriately labeling and scaling your own axes.
