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A manager’s job often calls for making very complicated decisions. Some decisions involve planning what products the business is to make and determining what resources are needed to make these products. In the modern business world, diversification of products provides a company with stability in a climate of changing tastes and needs. So it is not surprising that companies would produce many products, some of which share resource needs. For example, any bakery uses many resources—like butter, sugar, eggs, and flour—to make its products such as cookies, cakes, pies, and breads. Similarly, car manufacturers use many kinds of metals in the different models of cars they make, and manufacturers of gasoline use different kinds of crude oils to make their product.

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Resources can include more than just raw materials. Farmland, time, machinery, and a labor force with appropriate skills are also resources. Typically, resources are limited: A farmer owns only so much land; there are only so many hours in a day; in a year of drought the wheat crop is very small; a winter freeze may damage an orange crop. Resource availability is also limited by location and competition.

Because resources are limited, management faces important questions: How should the available resources be shared among the possible products and different parts of the company’s operation? One goal of management is to maximize profit. How can that determine how much of each product should be produced? There are usually so many alternative product mixes that it is impossible to evaluate them all individually. Despite this complexity, millions of dollars may ride on management’s decision.

Many business and government agencies must deal with supply-and-demand problems. The general idea is that goods or services can be provided by different providers to individuals or businesses who need these goods or services. There are varying costs to the suppliers to provide different recipients with these goods or services. The goal is to find how to meet the demands from the supplies as cheaply as possible. For example, what is the cheapest way for a company with several oil refineries to provide oil distributors, in many different geographical locations, with the oil they need? Perhaps surprisingly, ideas related to linear programming have also been used to help decide whether tumors are malignant or benign.