A company produces athletic shoes. For simplicity we assume that every month has 20 working days. Each day consists of 7 hours of regular time and each employee can work up to 3 hours of overtime per day. As of today the company employs 100 workers who are paid a fixed monthly salary of $1000 dollars. The firm pays $10 per overtime hour. Hiring a worker costs $400; firing a worker costs $3000. Every worker can assemble 2 shoes per hour. The holding cost is $1.35 per unit per quarter. A penalty cost of $100 per unit is incurred on lost sales. Firm wants to ellaborate a production schedule for the next 10 quarters as to meet all demand each quarter. Formulate then solve (use excel solver) a linear program aimed at minimizing the total cost for the firm. The solution should include for each quarter the number of workers hired/fired, the number of overtime hours, the number of shoes produced, and the quantity of inventory. In addition, it must specify the total hiring cost, total firing cost, total inventory cost, total fixed salary cost, total cost on lost sales (if any), total overtime cost and total cost of the plan for the whole planning horizon. Year Remaining of last year 2 Initial workforce Fixed monthly salary Overtime cost Holding cost Quarter Hiring cost Firing cost 3 4 1 2 3 4 1 2 3 4 Production per worker Stock-out cost Working Days 20 60 60 60 60 60 60 60 60 60 Forecast Demand (units) $1,000.00 2982 43489 96217 65036 16119 89764 187090 120211 28524 152952 100 workers $10.00 per hour $1.35 per unit per quarter $400.00 $3,000.00 2 units per hour $100.00 per unit per quarter