Flynn Commercial Freezer Ltd$.($FCF Ltd$),$ makes commercial and industrial freezers $($the kind hotels and restaurants use, and has the aggregate demand requirements for the next six months as given in the table below as are the costs and other necessary data. The firm has regular capacity for $480$ units, and overtime capacity for $40$ more. Currently, subcontracting can supply up to $100$ units per month and this is unlikely to change in the near future. Month

Demand Costs and other data

$1440$ Previous output level $460$ units

$2480$ Beginning inventory $0$ units

$3520$ Stockout cost $800$ per unit

$4500$ Inventory holding cost $400$ per unit at end of month

$5420$ Unit Cost, regular time $1,500$ per unit

$6400$ Subcontracting $2,100$ per unit

Unit Cost, overtime $1,800$ per unit

Hiring workers $200$ per unit

Firing workers $500$ per unit

FCF Ltd is considering one of the following three aggregate plans:

Plan A is to produce level quantity, incurring back orders and inventory charges, Plan B is to produce a base quantity of $480,$ using first, overtime, then subcontracting, to meet demand and Plan C$,$ a chase plan, using overtime and then subcontracting if regular capacity is insufficient to cover monthly demand.

The company wishes to minimise costs.

Note: there is no need to start and end on the same output level.

FCF Ltd has asked you to recommend one of the plans. Prepare each of the plans, calculate the costs associated with each plan and make a recommendation.