Please solve it manually. Do not use excel.

Soni produces two types of speakers: models A and B. It takes 1 and 2 manhours to produce model A and B respectively. The company currently has 16 employees who work 10 hours per day on regular time and can work another 2 hours of overtime per day when necessary. Due to union regulations, these workers cannot be fired. The regular hourly pay is 10 TL and overtime pay is 15. TL. Each worker is paid a minimum of 1010=100 TL per workday even if he is idle. If necessary, it is also possible to hire temporary workers on a monthly basis at 20TL per hour. You can also hire permanent workers at a cost of 1000 TL each, but these workers cannot be fired once they are hired. Assume 20 workdays per month and no significant hiring/firing costs for temporary workers. The inventory holding cost for both models can be approximated to be 3 TL per month per production hour incurred. Demand information for each model for the next 4 months is given below. a. (30 pts) Formulate an LP to minimize the total cost of production (labor and inventory holding) for the next 4 months. Assume that all demand must be met on time.You must define your variables clearly, write out the the constraints that must be satisfied explaining the significance of each, and write the objective function with explanation. b. (5 pts) How would you modify this formulation if it is possible to backlog demand, but there is a 50 TL monthly cost per each backlogged unit