Form an LP model based on this question. The model should contain an objective function having $60$ decisions variables, and $24$ constraints. The company is changing in ways that will impact its workforce needs in the coming years. New

machines will require fewer unskilled workers and more skilled and semi$-$skilled workers.

Additionally, a decline in sales is expected next year, which will reduce the need for workers across

the board. Forecast of manpower requirements for the next three years is tabulated below.

The company wants to develop policies for the following over the next three years:

Recruitment

Retraining

Redundancy

Short time working.

Employee turnover is a natural part of any workforce. A significant number of workers leave in their

first year, but the rate of turnover decreases significantly after that. Based on this, we can estimate

the following wastage rates:

The company has not hired any new workers recently, and all current employees have been with the

company for more than one year. The company is able to recruit a limited number of workers from

outside each year, as follows:

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 time as some training is done on the job. Retraining

a semi$-$ skilled worker in this way costs $500.$

Downgrading workers to a lower skill are possible but $50\%$ of such workers leave, although it costs

thecompany nothing. $($This wastage is additional to the 'natural wastage' described above$).$

The redundancy payment to an unskilled worker is $200$ and to a semi$-$skilled or skilled worker is

$500.$ It is possible to employ up to $150$ more workers over the whole company than are needed, but

the extracosts per employee per year are as follows:

An employee on short time working meets the production requirements of half a full$-$time 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.