The Trim-Look Company is evaluating its product lines to maximize profits. It produces skirts, dresses, and sport coats using fabric from its South Islander line. The cutting and sewing departments have limited hours and material is limited. Each product contributes different profits. A procurement manager must determine the optimal blend of three raw materials to produce additives. Each material has different combustion points, gamma and zeta contents. The manager aims to minimize costs while meeting product requirements. E-Traders investment firm has $5 million to invest across corporate bonds, common stock, gold certificates and real estate. The board requires at least 40% in corporate bonds and common stock, and no more than 20% in real estate.

1. 1. Application : Product Mix Problem
The Trim-Look Company makes several lines of skirts, dresses, and sport coats for women.
Recently it was suggested that the company reevaluate its South Islander line and allocate
its resources to those products that would maximize contribution to profits and overhead.
Each product must pass through the cutting and sewing departments. In addition, each
product in the South Islander line requires the same polyester fabric. The following data
were collected for the study.
Processing Time (hr)
Product Cutting Sewing Material (yd)
Skirt 1 1 1
Dress 3 4 1
Sport coat 4 6 4
The cutting department has 100 hours of capacity, sewing has 180 hours, and 60 yards of
material are available. Each skirt contributes $5 to profits and overhead; each dress, $17;
and each sport coat, $30.
2.
Blending Problem
A problem often of concern to managers in the process industry is blending. Consider the
task facing the procurement manager of a company that manufactures special additives.
She must determine the proper amounts of each raw material to purchase for the production
of a certain product. Three raw materials are available. Each gallon of the finished product
must have a combustion point of at least 220°F. In addition, the gamma content (which
causes hydrocarbon pollution) cannot exceed 6 percent of the volume. The zeta content
(which cleans the internal moving parts of engines) must be at least 12 percent by volume.
Each raw material has varying degrees of these characteristics.
Raw material
Characteristic A B C
Combustion point (oF) 200 180 280
Gamma content (%) 4 3 10
Zeta content (%) 20 10 8
Raw material A costs $0.60 per gallon; raw material B, $0.40; and raw material C,
$0.50. The procurement manager wishes to minimize the cost of raw materials per
gallon of product. What are the optimal proportions of each raw material to use in a
gallon of finished product? Hint: Express your decision variables in terms of fractions of
a gallon. The sum of the fractions must equal 1.00.
3.
Portfolio selection
E-Traders, Inc. invests in various types of securities. The firm has $5 million for immediate
investment and wishes to maximize the interest earned over the next year. Risk is not a
factor. There are four investment possibilities, as outlined below. To further structure the
portfolio, the board of directors has specified that at least 40 percent of the investment must
be placed in corporate bonds and common stock. Furthermore, no more than 20 percent of
the investment can be in real estate.

2. Investment Earned (%)
Corporate bonds 8.5
Common stock 9.0
Gold certificates 10.0
Real estate 13.0
DEFINITIONS
CBx = Millions of dollars invested in corporate bonds
CSx = Millions of dollars invested in common stock
GCx = Millions of dollars invested in gold certificates
REx = Millions of dollars invested in real estate