What will you learn?

$0$ Aggregate Production Plan

tade

Number of

Demand

$90$

$75$

$130$

Aggregate

A TV company produces Smart TVs$.$ The company wants to plan production and workforce levels for the next $5$ months. Above table shows the number of workdays and Smart TV demand $($in thousands$)$ for each month.

The inventory holding cost per Smart TV per month is calculated as $$15.$ If the company cannot satisfy a demand on time, a monthly backorder cost of $$25$ is incurred. Additionally, past data shows that $25$ workers can produce $60$ thousand Smart TVs in $20$ days. The company currently has $35$ workers. The company incurs a hiring cost of $$750$ and firing cost of $$1300$ per worker. The payroll is $$50$ per worker per day.

What is the number of workers needed if the company wants to apply a constant workforce plan where stock$-$outs are not allowed?

What is the total inventory holding cost for the constant workforce planwith the number of workers found in part $b?$

$-$Suppose that the company cannot change the number of workers that they have for the first $3$ months. In month $4$ or $5$ they can change the number of employees so that they widetilde$($ can $)$ satisfy the total demand. Propose a production and workforce ptan under these circumstances. Calculate the cost of this plan.

Write an LP that solves this problem.