this question has my stuck, I am unsure on how to incorporate the some of the information into constraints and without them the answer seems a bit silly. Below is the question, please let me know how you would go about formulating it:
Two aircraft, each with a capacity of 156 seats. The daily schedule of these aircrafts is shown in Table 1.
The company offers discounted (D-class) and full-fare class (F-class). D-class must be purchased two weeks in advance of flight departure and are non-refundable, non-changeable. F-class tickets can be purchased anytime and fully refundable and changeable. The prices and demands for both classes are given in Table 2.
The task is to formulate the problem of accepting reservations on different fare classes to maximize revenue as a linear programme.
I'm not even sure if table 1 has any useful information to this task.
Table $2$ gives $8$ possible journeys between various cities. Let the number of $D$ and $F$ class reservations for the $i^{\text{th}}$ journey be $d_i,f_i\ge0$. Then the first set of constraints is the upper-bound on $d_i,f_i$:$$d_1\le25,f_1\le20\\d_2\le55,f_2\le40$$and so on.
Both planes have a capacity of $156$, so on each stretch out of the $8$ stretches$(A\to B,B\to C,C\to B,B\to A;D\to B,B\to E,E\to B,B\to D)$, there must be $\le156$ passengers on either plane. For example, a passenger travels on the stretch $A\to B$ iff he/she takes any one of journeys $1,2,3$ and thus, $(d_1+d_2+d_3)+(f_1+f_2+f_3)\le156$.
Similarly, passengers travel on stretch $B\to C$ iff they undertake any one of journeys $2,5,7$; stretch $D\to B$ iff they undertake journeys $4,5,6$; stretch $B\to E$ iff they undertake journeys $3,6,8$.
The objective function to maximize is quite obviously the revenue given by $150d_1+200f_1+270d_2+400f_2+...+200d_8+300f_8$.
I solved the LPP in Excel and the solution I got is: