Operations Management: An Integrated Approach, 5th Edition

INTERPRETING THE SOLUTION

As shown in Figure B-11, the optimal solution is to make 100 camshafts and 350 gears. Doing so will yield a profit of $8800 and will require 3300 pounds of steel, 1000 hours of labor, and 1000 hours of machine time. Notice that we don't use all the steel that is available. In fact, there are 1700 pounds of steel unused. However, all of the labor and machine time is used. Having steel left over might seem nonintuitive, but making more of either camshafts or gears (to use up more steel) would also require more labor and machine time, of which we have no extra. Therefore, we are at a limit of sorts in how far we can “push” this solution. In general, if we have more constraints than decision variables, there will some constraints that are not at their limits. Constraints at their limits when at the optimal solution, that is, with the LHS value equal to the RHS value, are called binding constraints. Those that are not at their limits are called nonbinding constraints. Here the binding constraints are labor and machine time, and the nonbinding constraint is steel. As noted, we have 1700 pounds of steel remaining at this solution. This value is called the slack of the constraint and is simply the difference between the RHS value and the LHS value (slack values for binding constraints are equal to 0). This is a fundamental insight gained from the solution. Before solving the problem, we didn't know that labor and machine time would run out, in a sense, before ...