PROBLEM$-2)(20$ Pts$.)$ Due to strategic decisions of the high level management, The XYZ Tyre

Company is in the process of planning labor force requirements and production levels for the next four

quarters. The sales and marketing department of the XYZ Tyre Company has provided production with the

following forecasts of demand for XYZ Tyre Company over the next year:

Assume that there are currently $500$ employees with the company. Employees are hired for at least one full

quarter. Hiring costs amount to $$1,000$ per employee and firing costs are $$2,000$ per employee. Inventory

costs are $$1$ per package $(1500$ Tyres$)$ per quarter. It is estimated that one worker produces $1,500$ tyres each

quarter. Assume that XYZ Tyre Company currently has $80000$ of type A$,90000$ of Type B and $100000$ of

Type C tyres in inventory and would like to end the year with an inventory of at least $100000$ of type A$,$

$110000$ of Type B and $120000$ of Type Ctyres packages.

Determine the minimum constant workforce plan for XYZ Tyre Company and the cost of the plan.

Assume that stock$-$outs are not allowed. $(10$ Pts$.)$

a$.$ Suppose that the plant has the capacity to employ a maximum of $400$ workers. Suppose that regular$-$

time employee costs are $$10\mathrm{.}00$ per hour. Assume seven$-$hour days, five$-$day weeks, and four$-$week

months, three month$-$quarters. Overtime is paid on a time$-$and$-$a$-$half basis. Subcontracting is

available at a cost of $$5$ per tyre produced. Overtime is limited to four hours per employee per day,

and no more than $100,000$ tyres can be subcontracted in any quarter. Formulate as a linear

program. $(10$ Pts$.)$