For problems 1 to 3 below, develop a mathematical programming formulation. State whether your formulation is an LP,IP, MIP, or NLP and explain why. 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 ob 5 also. Formulate a mathematical program to find the optimum solution. For problems 1 to 3 below, develop a mathematical programming formulation. State whether your formulation is an LP,IP, MIP, or NLP and explain why. 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 ob 5 also. Formulate a mathematical program to find the optimum solution