The Reserve Crew Allocation Program is a linear program used by American Airlines to allocate and utilize reserve crews at a minimum cost. The program selects a set of crews to meet the daily demand for reserve crews. The number of reserves required on any particular day is forecast by using experience to establish probabilities. The simplex tableau is presented below. [ Figure 1 Image] The constraints are given by allx1 + a12x2 + a13x3 + a14x4 + + alnxn > b1. For example, the first row of the tableau corresponds to the constraint x1 + x4 + > 8, while the second row corresponds to x1 + x2 + > 7. The cost function to be minimized is w = c1x1 + c2x2 + c3x3 + + cnxn. The linear programming example of reserve crew allocation discussed above is American Airline's own program. They also use a standard linear program to schedule their flight crews on aircraft and for training assignments. This is a considerably larger and more complicated program. Exercises 1.