AOE/ESM 4084 - ENGINEERING DESIGN OPTIMIZATION

Fall Semester, 2000

Homework Assignment 2

Due 2.00 PM, Tuesday, September 12

A soft-drink company has a new drink that they plan to market. Through their preliminary research, it was found that the cost C to produce and distribute a cylindrical can for the drink is approximately

,

where V_o is the volume in fluid ounces, and S is the surface area of the can in square inches. They also determined that they can sell the drink in cans ranging from 5 to 15 ounces, and then the price P in cents that can be charged for a can is estimated as

.

Based on their past experience they will consider only a can with diameter D between 1.5 and 3.5 inches, and their market research has shown that soft-drink cans have to have an aspect ratio of at least 2.0 to be easy to drink from. That is, the height H of the can has to be at least twice the diameter.

The objective of the company is to design the can to maximize their profit from the sales of the soft drink. Two measures of profit are considered. One is the profit per can, and the other is the profit per ounce of the drink. The first measure is more useful if we assume that consumers will buy a fixed number of cans, and the other if we expect consumers to buy a fixed volume of drink.

a) Formulate the design optimization problem for maximizing the profits, and solve for the optimal values of the can diameter and height for each of the objective functions.

b) Generate the Pareto optimal curve for the problem.

c) Determine the design that minimizes sum of the squares of d_i, where

and show it on the Pareto optimal curve.