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36 CHAPTER 2 AN INTRODUCTION TO LINEAR PROGRAMMING

Table 2.1 Production Requirements Per Golf Bag
Production Time (hours)
Department Standard Bag Deluxe Bag

Cutting and Dyeing 7 / 10 1
Sewing 1 / 2 5 / 6
Finishing 1 2 / 3
Inspection and Packaging 1 / 10 1 / 4

The director of manufacturing analyzed each of the operations and concluded that
7
if the company produces a medium-priced standard model, each bag will require / 10
1
hours in the cutting and dyeing department, / 2 hour in the sewing department, one
1
hour in the finishing department, and / 10 hour in the inspection and packaging
department. The more expensive deluxe model will require one hour for cutting
1
5
2
and dyeing, / 6 hour for sewing, / 3 hour for finishing, and / 4 hour for inspection
and packaging. This production information is summarized in Table 2.1.
Production is constrained by the limited number of hours available in each
department. After studying departmental workload projections, the director of
manufacturing estimates that 630 hours for cutting and dyeing, 600 hours for sewing,
708 hours for finishing and 135 hours for inspection and packaging will be available
for the production of golf bags during the next three months.
The accounting department analyzed the production data, assigned all relevant
variable costs and arrived at prices for both bags that will result in a profit contri-
1
bution of $10 for every standard bag and $9 for every deluxe bag produced.
It is fairly clear what the decision problem is that the company faces: how many of
It is important to
understand that we are the two types of golf bag should it manufacture in order to maximize profit con-
maximizing profit tribution? What is less clear is the answer to the problem. This is where LP can help
contribution, not profit. and we will work through a number of stages. First, that of problem formulation,
Overhead and other
shared costs must be where we produce a mathematical statement of the LP problem. Then that of
deducted before arriving problem solution, where we find the answer to the decision problem we are looking
at a profit figure. at. Finally, that of interpretation, where we consider what the company should do.

Problem Formulation

Problem formulation or modelling is the process of translating the verbal statement
of a problem into a mathematical statement. Formulating models is an art that can
only be mastered with practise and experience. But even though every problem has
some unique features, most problems also have common features. As a result, some
general guidelines for model formulation can be helpful, especially for beginners.
We will illustrate these general guidelines by developing a mathematical model for
the GulfGolf problem.

Understand the Problem Thoroughly We selected the GulfGolf problem to
introduce linear programming because it is easy to understand. However, more
complex problems will require much more thinking in order to identify the items that
need to be included in the model. In such cases, read the problem description quickly to
get a feel for what is involved. Taking notes will help you focus on the key issues and facts.

1
From an accounting perspective, profit contribution is more correctly described as the contribution margin per
bag; for example, overhead and other shared costs have not been allocated.

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