$1)$ Develop an aggregate production plan for a furniture producer based on the following information. Define the Total Cost for each plan.

Cost and Production Information

Regular production cost $=$ $$50$ per unit

Overtime production cost $=$ $$75$ per unit

Subcontracted production cost $=$ $$100$ per unit

Inventory holding cost $=$ $$10$ per unit per month

Backorder cost $=$ $$20$ per unit per month

Hiring cost $=$ $$200$ per worker hired

Termination$/$Firing cost $=$ $$150$ per worker terminated

Overtime production limit $=$ max of $100$ units per month

Production rate $=30$ units per worker per month

Opening inventory level $=120$ units

Opening workforce level $=45$ employees

The Demand for each one of the $6$ months is defined on the tables below

$1$a$)$ Adopt the Level Approach using the Average Demand to be the constant production rate. You can use inventories

and backorders. What is the total cost of this Aggregate Plan?

Period Demand Total Prod. Workforce Inventory Reg. Prod. Overtime Subcontr. Hire Fire

$045120$

$11000$

$21200$

$31500$

$41800$

$51600$

$61300$

Hiring & FiringProduction BreakdownAggregate Production Plan

$1$b$)$ Adopt the Chase Approach. You can use hiring and firing, but not overtime or subcontracted production.

What is the total cost of this Aggregate Plan?

Aggregate Production Plan Production Breakdown Hiring & Firing

Period Demand Total Prod. Workforce Inventory Reg. Prod. Overtime Subcontr. Hire Fire

$045120$

$11000$

$21200$

$31500$

$41800$

$51600$

$61300$

$1$c$)$ Modify $1$a $$ keep the initial workforce level and use overtime and subcontracted production as needed,

no backorders $($no hiring or firing$).$ What is the total cost of this Aggregate Plan?

Period Demand Total Prod. Workforce Inventory Reg. Prod. Overtime Subcontr. Hire Fire

$045120$

$11000$

$21200$

$31500$

$41800$

$51600$

$61300$

Aggregate Production Plan Production Breakdown Hiring & Firing

$1$d$)$ Modify $1$b $$ limit the number of hiring to max of $7$ in each month $($no overtime or subcontracted production$).$

What is the total cost of this Aggregate Plan?

Aggregate Production Plan Production Breakdown Hiring & Firing

Period Demand Total Prod. Workforce Inventory Reg. Prod. Overtime Subcontr. Hire Fire

$045120$

$11000$

$21200$

$31500$

$41800$

$51600$

$61300$

Question$1$: What is the best approach to adopt: pure leve $(1$a$)$ or pure chase $(1$b$)?$ Why? Which production factor$($s$)$ contribute$($s$)$ to this choice?

Question$2$: What is the best Aggregate Plan among those $4$ plans executed above? Why? Which production factor$($s$)$ contribute$($s$)$ to this choice