Problem $2.$ Sailco Production Planning

Sailco needs to determine the appropriate production quantity of sailboats for each of the next

four quarters. The sales and production data from the past $10$ years can be found in Figure $1$ and

are also available in the Sailco$\_$Data.xlsx file.

The sailboat product has been highly profitable, with a selling price of $$2000$ per unit and a

production cost of $$1200$ per unit.

During the first seven years, Sailco's production capacity allowed for a maximum output of $500$

units per quarter. However, due to a consistent increase in demand, Sailco expanded its capacity

to $600$ units per quarter starting from Year $8.$ Typically, the production capacity is not fully

utilized. In Quarter $2$ of Year $9,$ Sailco exceeded its regular capacity by producing more than $650$

sailboats, employing overtime for their employees. This resulted in an additional cost of $$200$ per

unit for each sailboat beyond the regular production capacity.

Sailco strives to meet customer demand promptly. For simplicity, we assume that sailboats

produced during a quarter can fulfill the demand for that quarter as well as future quarters. In

some cases, the production quantity is lower than the demand for a particular quarter. This is

because Sailco has previously produced more than the demand in earlier quarters, resulting in

inventory that can be used to meet future demand. However, it is important to note that holding

inventory incurs costs. At the end of each quarter, after production has taken place and the

demand for the current quarter has been met, a holding cost of $$60$ per sailboat is incurred.

How can you assist the production manager in devising a production plan for the next four

quarters?