OS / Linear Programming

τ1 = (70, 26, 70), τ2 = (84, 31, 84), τ1 = (60, 11, 60) where t1, t2 and t3 are period, computation time and deadlines respectively. Find an arbitrary non-preemptive schedule of the tasks. To make the problem simple, it is assume that the first instance of the three tasks {τ1, τ2, τ3} are invoked at time zero. Try to use integer linear programming framework to find the schedule.

Hint: Find the LCM of all the periods and devise constraints for every deadline requirement within the LCM period.