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 1Dress 3 4 1Sport 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 10Zeta 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.

Investment Earned (%)Corporate bonds 8.5Common stock 9.0Gold certificates 10.0Real estate 13.0

DEFINITIONS

xCB= Millions of dollars invested in corporate bondsxCS= Millions of dollars invested in common stockxGC= Millions of dollars invested in gold certificatesxRE = Millions of dollars invested in real estate