Suppose you are a manufacturer of human powered vehicles. You have a given schedule of demands for finished products over time. You need to know when and how many of each component, subcomponent, etc. is needed to meet demand.

Your final products are as follows:

1.Unicycles, made from a seat and a wheel,
2.Bicycles, made from a seat, two wheels, and a chain, and
3.Tandems (bicycles built for two), made from two seats, two wheels, and two chains.

Each product is assembled from a set of components. Each com­ponent in turn may be assembled from other subcomponents. For simplicity and generality, we will refer to all products, components and subcomponents as parts.

The subcomponents are as follows:

1.Seats,
2.Wheels, made from a hub and 36 spokes,
3.Chains, made from 84 links,
4.Hubs,
5.Spokes, and
6.Links.

It takes a certain amount of time, called the lead time, to produce each batch of parts. The component parts for each part must be on hand when you begin production of a part.

The sales department has estimated demand for two months (eight weeks) in the future. According to their findings, there will be a demand for 10 unicycles in week eight, and 20 bicycles and 20 tandems in week nine.