Reserve Crew Allocation ProgramtThis application uscs concepts coverod in Chapter $4.$The Reserve Crew Allocation Program is a linearused by American Airlines to allocate and utilizereserve crews at a minimum cost. The program selcctsa 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.The constraints are given byAvailable crewswhile the second row corresponds toTThe cost function to be minimized isExercises$00$In the tableau, d$.,00$ Iif crew $,$ is on duty on dayotherwiseb minimum umberrequired on day $4$For example, the first row of the tableau corresponds to the constraint$28,$Min costax taj$21)$ t ajy t ajgX$4$ t tajnn bj$-$of reserve crewsThe lincar programming example of reserve crew allocation discussed above is American Airline's ownprogram. They also use a standard linear program to schedule their flight crews on aireraft and for trainingassignments. This is a considerably larger and more complicated program$\mathrm{.}1.$ Suppose there are $4$ crews available. Crew $1$ is on duty days $1$ and $2.$ Crew $2$ is on duty days $1$ and $3.$ Crew $3$is on duty days $2$ and $3.$ Crew $4$ is on duty days $1,2,$ and $3.$ A minimum of $2$ crews is required on days I and