A manufacturer builds finished items A, B, and C from five different components. They currently have several finished units, a number of items that are partially complete, and many components that have just been delivered from their suppliers
The finished items, incomplete items and raw components can all be assigned some monetary value even though the manufacturer typically does not sell anything except finished items. The manufacturer needs to raise capital quickly so they formulate a linear program to help them decide on the most profitable way ahead. Their linear programming expert forgets to restrict their decision variables to non-negative values and is surprised when the computer output tells them that finished item A and C should be negative. If the company always follows the advice of their linear programming analysis, what should they do and why?
The assumption of nonnegativity is that decision variables must either be positive or zero. In this case, it would appear that either a) the components are more valuable to the company than the finished items (perhaps there is a pricing error and the company is not charging enough for their products) or b) disassembling items A and C might yield parts that could be used to produce item B, which is a more profitable product. Depending on the values of the other decision variable, the company should begin disassembly of finished items A and C. They might also ask their linear programming analyst to update his resume.
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