PROBLEM$-3)(20$ Pts$.)$ The Sales&Operations $($S&OP$)$ process is designed to produce a plan that all departments within the organization, as well as suppliers to the organization, can work. The process is also sometimes referred to as sales, inventory, and operations planning $($SIOP$)$ to emphasize the important role that inventory can play as a buffer between sales planning and operations planning. The S&OP department of the XYZ company, that produces KLM products, estimates the sales over the next six years in thousands of packages will be as follows:

$\backslash$table$[[$Year$,\backslash$table$[[$Forecasted Demand$],[($Thousands of Packages$)]]],[1,2400],[2,960],[3,1600],[4,880],[5,1080],[6,1600]]$

Assume that each worker stays on the job for at least one year and XYZ currently has eight workers. XYZ estimates that they will have $600000$ packages on hand at the end of the current year. Assume that, on average, each worker is paid TL $60000$ per year and is responsible for producing $80000$ packages. Inventory costs have been estimated to be $20KRS$ per package per year, and shortages are not allowed. XYZ estimates that it costs TL $2500$ for each worker hired. Severance pay amounts to TL $3,000$ per worker.

a$.$ Assuming that shortages are not allowed, determine the minimum constant workforce that he will need over the next six

$2$

years. $($Io pts$)$

b$.$ Formulate this as a linear program. $($Io pts$)$