Chick$-$fil$-$A is preparing its aggregate plan for the first six months of $2023.$ The tables below contain the monthly demand forecast, working days per month, and cost information.

Month Expected Demand Production Days

January $18020$

February $16020$

March $22010$

April $15010$

May $25025$

June $24015$

Inventory carrying cost $15$ per unit per month

Subcontracting cost per unit $30$ per unit

Regular working hours per day $8$ hours

Labor$-$hours to produce a unit $2$ hours$/$unit

Average pay rate $10$ per hour

Overtime pay rate $15$ per hour

Cost of increasing daily production rate $($hiring and training$)150$ per unit

Cost of decreasing daily production rate $($layoffs$)200$ per unit

The company is considering the following three strategies:

Plan $1$: A constant workforce, daily production rate $=$ average requirements

Plan $2$: Main a constant workforce at a necessary level to meet the lowest requirement, and to meet all demand above this level by subcontracting.

Plan $3$: Hire and layoff workers as needed to produce exact requirements