Product mix decisions are essentially resource allocation problems. We have limited resources, such as machines, labor, and raw materials, and the problem calls for their optimal use in order to maximize profit, which is earned by producing and selling a set of items. The decision problem consists of finding the right amounts to produce for each item over a certain timespan. Profit depends on the cost of producing each item and the price at which they can be sold. Produced quantities should comply with several constraints, such as production capacity and market limitations, since we should not produce what we are not going to sell anyway.
One of the fundamental pieces of information we need is demand. The time period we work with can be a day, a week, or a month. In practice, demand varies over time and can be quite uncertain. Here we consider an idealized problem in which demand is known and constant over time. Furthermore, demand is not completely exogenous in real life, as we might influence it by pricing decisions. Price can be more or less under direct control, depending on the level of competition and the type of market we deal with; in a product mix problem we typically assume that we are price takers.
In the first example below, products are similar in the sense that they consume similar amounts of resources. In the second one, we will complicate resource consumption a bit.
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