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Product Mix

Problem: Using available resources to manufacture a mix of products which yield the highest profit.

In product mix problems, the objective is to find the most profitable allocation of a set of limited resources over a set of desired products or activities. Virtually every manufacturer faces this situation in some form or other.

This example involves the conversion of raw materials into manufactured goods. An agricultural example might involve the use of land, seed, water, labor, and fertiliser so as to maximise farm output. Product mixing problems often serve as the "building blocks" for more complex applications.

You are a manufacturer producing six products from six materials with each product requiring a different combination and amount of raw materials.

You know the profit per unit of each product and the quantity of each raw material required for a single unit of each product. For instance, each unit of Product 2 contributes $45 to profit and uses 4 units of steel, 5 of wood, 3 of plastic, etc. in its manufacture.

The objective of optimisation is to maximise the profits that can be realised from manufacturing products using only the current inventory of raw materials.

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