$($b$)$ You are the scheduling coordinator for a

small, growing airline. You must schedule

exactly one flight out of Bengaluru to each of

the following cities: New Delhi, Kolkata,

Mumbai and Chennai. The available

departure slots are $8$ A$.$M$.,10$ A$.$M$.,$ and

$12$ noon. Your airline has only two departure

lounges, so at most two flights can be

scheduled per slot. Demand data suggest the

following expected profit contribution per

flight as a function of departure time:

Expected Profit Contribution in Rs$.1,000$s

Time

Formulate an integer programming model

for this problem.