The Vice President of Operations of a tractor company has asked your team to develop a production schedule for their tractors over the next quarter.

The marketing department has prepared a forecast of the number of tractors needed for the next three months (250 tractors in month 1, 305 tractors in month 2, and 350 tractors in month 3). Your job is to prepare an production schedule to produce the required number of tractors at minimum cost.

The company has employees that can work regular-time and overtime to produce the tractors. Each tractor requires 100 labor hours to produce. A total of 29,000 regular-time labor hours are available each month to produce the tractors. The regular-time labor cost rate is $20 per hour and the overtime labor cost rate is 150% (time-and-a-half) of the regular-time cost rate. The number of overtime hours used can't exceed 10% of the regular-time labor hours used in a given month.

The company has a warehouse where tractors can be produced, stored, and sold in a later month. The warehouse can store up to 40 tractors. A carrying cost of $600 is charged each month a tractor is stored in inventory. There are no tractors in inventory at this time.

question:

You must provide a description of the decision variables, the objective function, and the constraints. Also, add in the cost saving formula