The personnel department of a company wants to know how many workers will be needed each month

for the next six$-$month production period. The following table shows the monthly demand forecast for the

six$-$month period.

The inventory on hand at the end of June was $500$ units. The company wants to maintain a minimum

inventory of $300$ units each month and would like to have $400$ units on hand at the end of December.

Each unit requires $5$ employee$-$hours to produce, there are $20$ working days each month, and each

employee works an $8-$hours day. The workforce at the end of June was $35$ workers. Assume Hiring cost

$=$$$500$ and Firing cost $=$$$1,000$

a$)$ Determine a minimum inventory production plan $($chase strategy$)$

b$)$ Determine the total cost for part a

c$)$ Determine the level production plan that meets demand but does not hire or fire workers during the

six$-$month period.

d$)$ Determine the total cost for part c

e$)$ Construct the LP model for the problem and determine the optimal solution using LINDO