An FBO (a \"fixed-base-operator\", usually the manager of a small-town airport)

Question

An FBO (a "fixed-base-operator", usually the manager of a small-town airport) makes his revenue in three ways: flight instruction, charter flights, and aircraft maintenance. These activities earn revenues of $25/hour, $40/hour, and $35/hour respectively. The FBO has enough work to guarantee at least 40 hours of work per week. He also, for reasons of sanity and family, refuses to work more than 60 hours per week. He has at least ten hours of each activity to do each week, but refuses to more than twenty hours of any one of these activities to keep himself from getting bored with any one activity. How should he schedule his time to maximize his revenue?

a) Formulate this problem using a linear programming model.
b) Solve this model by using graphical analysis.

Explanation / Answer

Let the time spent by FBO in flight instruction, charter flights, and aircraft maintenance be x1 , x2, x3 respectively.

he has to maximize his revenue "z".

so, the objective function is:-

maximize z = 25*x1 + 40*x2 + 35*x3.

subject to constraints: x1 + x2 + x3 >= 40;

                                  x1 + x2 + x3 <= 60;

                                   x1               >= 10;

                                      x2        >= 10;

                                   x3 >= 10;

                                   x1               <= 20;

                                          x2         <=20;

                                                 x3 <=20.

the formulation cannot ve done by graphical method as there are 3 variables.

however, by solving it by simplex alforithm, we get(x1 , x2 , x3) = (20 , 20 , 20)

hence, z = 2000

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