In a calculated financial move, Autojet has acquired a new manufacturing plant to produce small electric motors. You have been asked to answer the following question: 

How many new staff should be hired and trained, or fired, during each of the next six months? 

The labor requirements and monthly wage rates for trained manufacturing employees are given in the table below.

	Jan	Feb	Mar	Apr	May	Jun
monthly salary rate	$3500	$3500	$3800	$3800	$4100	$4100
Manufacturing hours required	7900	7600	9100	9800	8800	7400

Trainees can be hired at the beginning of each month. One consideration to keep in mind is that workers must have a month of training before they can work in manufacturing. Therefore, an apprentice must be hired one month before the worker is actually needed. Each trainee uses 50 hours of a trained manufacturing employee's time, making 50 fewer hours available for manufacturing. Each trained employee can work up to 170 hours per month (full time, training or in manufacturing). Management can lay off a maximum of 15% of the trained employees at the beginning of the month, but must pay half of that month's salary as severance pay. An apprentice is paid 40% of the regular salary of a trained employee during their training month. There are 48 trained employees available at the beginning of January. Formulate and solve this model of hiring, training, and firing as a spreadsheet mode of linear programming.