Problem $5($adapted from Taha, $2003)$: Razorback Airlines needs to assign aircraft to satisfy demand for

four routes. Each day, the demands for routes $1,2,3,$ and $4$ are $1200,1900,800,$ and $1300$ customers.

Razorback Airlines has three types of aircraft that can be used to satisfy this demand. The following

table provides the relevant data about each type of aircraft:

Depending on which route an aircraft is assigned, it may be able to complete the route multiple times in

a day. The following table specifies the number of times in one day an aircraft of each type can

complete each route:

The cost per trip on a route also depends on the aircraft. This data is given in the following table:

For each customer of unsatisfied demand on routes $1,2,3,$ and $4,$ respective penalties of $$240,$$$280,$

$$295,$ and $$400$ per customer are incurred due to lost sales.

Part a: Formulate a linear program to determine an aircraft$-$to$-$route allocation that minimizes costs.

$($Please go ahead and include integrality restrictions on your variables even though this technically

means your model is no longer a linear program.$)$ In this part, you should not use summation and "for

every".

Part b: Formulate an indexed linear program $($i$.$e$.,$ using summation and "for every"$)$ to determine a

minimum$-$cost plan for allocating aircraft to routes. You will need to define parameters to represent all

of the data associated with each aircraft type and route.

Part c: Solve the problem using an indexed model $($i$.$e$.,$ with summation and "for every"$)$ in AMPL$/$CPLEX

and report the obtained optimal solution.