please i need main models equations

Case 5 Manpower planning Part 1 The Problem A company is undergoing a number of changes which will affect its manpower requirements in future years. Owing to the installation of new machinery, fewer unskilled but more skilled and semi-skilled workers will be required. In addition to this a downturn in trade is expected in the next year which will reduce the need for workers in all categories. The estimated manpower requirements for the next three years are as follows: Current strength Year 1 Year 2 Year 3 Unskilled 2000 1000 500 Semi-skilled 1500 1400 2000 2500 Skilled 1000 1000 1500 2000 0 The company wishes to decide its policy with regard to the following over the next three years: (1) Recruitment (2) Retraining (3) Redundancy (4) Short-time working There is a natural wastage of labor. A fairly large number of workers leave during their first year. After this the rate is much smaller. Taking this into account, the wastage rates can be taken as below: Semi-skilled Unskilled 25% 10% Less than one year's service More than one year's service 20% Skilled 10% 5% 5% There has been no recent recruitment and all workers in the current labor force have been employed for more than one year. Recruitment It is possible to recruit a limited number of workers from outside. In any one year the numbers which can be recruited in each category are: Unskilled 500 Semi-skilled 800 Skilled 500 Retraining It is possible to retrain up to 200 unskilled workers per year to make them semi-skilled. This costs 400 per worker. The retraining of semi-skilled workers to make them skilled is limited to no more than one quarter of the skilled labor force at the times as some training is done on the job. To retrain a semi-skilled worker in this way costs 500. a Downgrading of workers to a lower skill is possible but 50% of such workers leave, although it costs the company nothing. (This wastage is additional to the natural wastage described above.) Redundancy The redundancy payment to an unskilled worker is 200 and to a semi-skilled or skilled worker 500 per employee per year. Overmanning It is possible to employ up to 150 more workers over the whole company than are needed but the extra costs per employee per year are: Unskilled 1500 Semi-skilled 2000 Skilled 3000 Short-time Working Up to 50 workers in each category of skill can be put on short-time working. The cost of this (per employee per year) is: Unskilled 500 Semi-skilled 400 Skilled 400 An employee on short-time working meets the production requirements of half an employee. The company's declared objective is to minimize redundancy. How should they operate in order to do this? If their policy were to minimize costs, how much extra would this save? Deduce the cost of saving each type of job each year