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Another Linear Programming Example:

Bicycle Wheels

Free Wheelers, Inc. makes spokes and rims for mountain bike wheels.
Recently, the firm has also started selling assembled wheels.

Each spoke requires 0.04 hours of machine time and 0.01 hours of
labor, and costs $0.05 to make. Each rim requires 0.6 hours of
machine time and 0.5 hours of labor, at a cost of $4.00.

An assembled wheel requires one rim and 72 spokes. Assembling a wheel
takes 1.2 hours of labor, in addition to that needed to make its rim
and spokes; no further machine time is needed. The assembly process
also incurs additional direct costs of $11.00.

Up to 378 hours of machine time and 267 hours of labor are available per week.

Assembled wheels sell for $50.00. Spokes not used to make assembled
wheels can be sold for $0.10 each. Similarly, rims not used in
assembled wheels can be sold for $10 each. Assume that, at these
prices, the firm can sell all the products it can produce.