PROJECT $2$

Red Bilgisayar is a company that manufactures personal computers and sells directly to customers.

Orders are accepted by telephone or through the company's website. Red Computer management will be introducing several new laptop models over the next few months and has recognised the need to develop technical support staff to specialise in the new laptop systems. One option being considered for a solution is to recruit new employees and put them through a three$-$month training programme. Another option was to put existing customer service specialists through a two$-$month training programme on the new laptop models. Red Computer estimates that the need for laptop specialists will increase from O to $100$from May to September as follows:

$$May$-20$; June$-30$; July$-85$; August$-85$; and September$-100.$After September, Red Computer hopes that it will be sufficient to maintain a staff of $100$laptop specialists.

The annual salary for a new employee, whether recruited for the training programme or replacing an existing employee who is being recruited for the training programme, is TL $48000.$The annual salary of the existing Red Computer employees who are considered to be included in the training programme is approximately $67000$TL$.$The cost of a three$-$month training programme is $3000$TL per person and the cost of a two$-$month training programme is $2000$TL per person. It should be taken into account that the length of the training programme will create a lag between the time when a new person is recruited and the time when a new laptop specialist is available. There is a limit to the number of existing employees who may be considered for training. Red Computer anticipates that the following numbers of staff will be available in the coming months:

March$-15$; April$-20$; May$-0$; June$-5$; and July$-10.$

The training centre has the capacity to start new three$-$month and two$-$month training courses each month; however, the total number of students $($new hires and current employees$)$starting training each month cannot exceed $25.$

Red Computer needs to determine the number of new employees who must start the three$-$month training programme each month and the number of existing employees who must start the two$-$month training programme each month. The aim is to meet the staffing needs from May to September at the lowest possible total cost, i$.$e$.$minimising the incremental salary cost and the total training cost.

As we are in January, and Red Computer is planning to hire new hires and existing employees.

would like to develop a plan to specify the distribution of participation in the training programme and the recruitment of new employees.

Management Report

Analyse the Red Computer problem and prepare a report summarising your findings.

$1.$Create a mathematical model to assist the manager by using linear proggramming.