Question: The Thomas Lee Paint Company is in the process of planning labor force requirements and production levels for the next six quarters. The marketing department has provided production with the following forecasts of demand for Thomas Lee over the next six quarters: 38000, 63000, 22000, 16000, 25000 and 20000. The Paints needed in a given quarter can be produced during that quarter. Paint can also be produced in earlier quarters and held in inventory until they are needed. The company has no paint on hand now, and it wants to have none in inventory at the end of planning horizon. Assume that there are currently 90 trained employees with the company and it needs to employ exactly 100 trained employees at the end of planning horizon. Each trained employee can make 1800 gallon of paint per quarter without working overtime. The normal work day is eight hours long and overtime is limited to two hours per employee per day. While working overtime, trained employees make paint at the normal rate. Trainees make only 1000 gallons of paint during their training period, which takes one quarter. Trainees are not allowed to work overtime. Workers can be hired and fired effective on the first day of each quarter. The costs are as follows. Wage costs total $4000 per employee per month and overtime is paid on a time-and-a-half basis. Employees are hired for at least one full quarter. Firing costs amount to $7000 per employee. It costs $3000 to hire and train a worker, not counting that person's lost productivity during training. It costs $4 to hold each gallon of paints in inventory each month. This inventory carrying cost is applied to each gallon of paints that is on hand on the first day of the quarter. Thomas Lee would like to determine a policy that meets the demand and minimize cost.
(a) Formulate a linear program to solve this problem. Define your decision variables and explain the constraints. Make sure that the numbers of workers fired are integer value in your formulation.
(b) Solve the linear program.HINT: For accounting purpose, the end of any quarter is the same as the beginning of the next quarter.