Problem 1. A machine shop manager needs to assign eight jobs among two available workers. The durations of the jobs are 40, 15, 25, 25, 45, 30, 35, and 60

minutes,respectively. Each worker has two and a half hours left available in their shifts. The manager would like to distribute the jobs among the two workers such that the total time worker 1 spends working on jobs during the last 30 minutes of their shift is kept to a minimum so that worker 1 can fill out paperwork. However, if a worker is assigned job 8,they cannot be assigned job 5 also. Formulate a mathematical program to find the optimum solution.