Decision variables for a linear program are:

E_aiq number of experienced pilots that fly only aircraft a, at installation i, during quarter q.T_aq number of pilots training to fly aircraft a, during quarter q (not experienced pilots). Y_aiq a binary variable with value 1 if there are pilots that fly only aircraft a at installation i during quarter q.

X_aq a binary variable with value 1 if pilots are training to fly aircraft a, during quarter q.

where a =1,2,3,4,5; i =1,2,...,8; and q =1,2,3,4.

Use summation notation and for all notation to write expressions for each of the following systems of constraints in terms of these decision variables, and determine how many constraints belong to each system.

1. a) Each quarter, ensure there are at least 2000 experienced F18 pilots (aircraft a = 3).

2. b) If Y_aiq= 0, then E_aiq= 0, but if Yaiq= 1, then E_aiq 120.

3. c) If X_aq= 0, then T_aq= 0, but if X_aq= 1, then 50 Taq 250 .

4. d) For each aircraft, train pilots in at least two quarters.

5. e) For each aircraft, train pilots in quarter 3 only if you train pilots in quarter 2.

6. f) In quarter one, train F18 pilots (aircraft a=3) or have experienced F18 pilots in Monterey (installation i= 2), but not both.