The Paint Company is in the process of planning
labor force requirements and production levels for the next four quarters. The
marketing department has provided production with the following forecasts of
demand for the company over the next four quarters: 380000 630000 220000 and 160000.
Assume that there are currently 300 employees with the company. Employees are
hired for at least one full quarter. Hiring costs amount to$1200 per employee and firing costs are $2500 per
employee. Inventory costs are one dollar per gallon per quarter. It is
estimated that one worker produces 1000 gallons of paint each quarter. Assume
that Paris
currently has 80000 gallons of paint in inventory and would like to end the
year with an inventory of at least 20000 gallons. Suppose that the plant has
the capacity to employ a maximum of 370 workers. Suppose that regular-time
employee costs are $12.50 per hour. Assume seven-hour days five-day weeks and
four-week months. Overtime is paid on a time-and-a-half basis. Subcontracting
is available at a cost of $7 per gallon of paint produced. Overtime is limited
to three hours per employee per day and no more than120000 gallons can be subcontracted in any quarter.
Paris would
like to determine a policy that meets the demand and the cost of that policy.(a) Formulate a linear program to solve this
problem.Define your decisionvariables
and explain the constraints.(b) Solve the linear program (use excel solver)