Part three:

Reconsidering the TechLink data in Exercise $1,$ assume that

the plant has $1,250$ employees and maintains a no$-$layoff

policy. Overtime is limited to at most $20$ hours per

employee per month, and there is no subcontracting option.

TechLink has a team of $50$ individuals willing to work as

seasonal employees. The cost of bringing them on is $800$

euros per employee, and the layoff cost is $1,200$ euros per

employee.

i$.$ Determine the optimal production, hiring, and layoff

schedule.

j$.$ Explore how the optimal schedule changes if the seasonal

pool grows from $50$ to $100.$

k$.$ In comparison to having $1,250$ permanent and $50$

seasonal employees, assess whether TechLink would

significantly benefit from carrying only $1,100$ permanent

employees but having $200$ seasonal employees.

Consider the case in which TechLink has $1,250$

permanent employees and $50$ seasonal employees. Does

TechLink gain more by eliminating its no$-$layoff policy

for its permanent employees or by increasing the

seasonal employee pool from $50$ to $100?$ Assume that

permanent employees can be hired or laid off at the same

cost as the seasonal employees.