A manufacturer employs skilled workers to make its wooden product. At the beginning of January, it has 15 skilled workers. Each skilled worker can work 200 hours per month. The labor hours
required for the next 6 month are as follows. The total hours available from skilled workers can be more than the labor hours required, leaving some hours idle, otherwise extra workers can be laid off at a cost.
Each skilled worker costs $4,000 per month. Hiring a new worker as a trainee costs $3,000. In addition, a trainee is paid $2,000 for the first month and is not involved in production. A trainee becomes a skilled worker starting in the following month. The manufacturer can lay off skilled workers at the beginning of a month, but must pay $3,000 for severance. How many trainees should be hired and how many skilled workers should be laid off each month to minimize the total cost?
a) Formulate the problem as a linear program on the spreadsheet.
b) Solve it using the Solver. What is the total cost over the 6 months?
c) In the optimal solution obtained in question (b), answer the following questions for April: how many skilled workers are continuing skilled workers from March? How many skilled workers are from trainees in March? How many new trainees are hired? How many workers are let go at the beginning of April, if any?