Joseph runs a water tank manufacturing operation called The Tank Company. The tanks are durable, can handle accidental freezing and can store liquids in food$-$safe certified plastics. It$$s a very busy operation and was recently on the cover of Operations Management magazine.

Joseph's production manager is Dina and has been asked to build a capacity plan either as a level, chase or mixed plan. Joseph made it clear that he wants the lowest cost per unit.

"The lowest cost is always boss" he would tell his staff when he did his morning $7$:$55$ am production meeting with his production teams. The staff were tired of Joseph's dad$-$type jokes, but they did understand the direction they were being given" KEEP COSTS AS LOW AS POSSIBLE". They also understood that Joseph was extremely cautious about quality. Joseph, although passionate about production and meeting timelines, Joseph was extremely sensitive to quality issues that arose occasionally. His true focus was on quality product, but he wanted to control production costs as this is what his bosses focused on$.$

Dina consults the production team, and they tell her they work best, and plan best, when they have a consistent workflow of regular activities. $($This sounds like one of her classes from her IBM$1000$ college course.$)$

Later that day she approached the sales manager Caroline, and asked her about the customer$$s needs. She told them she would have a delivery plan by the end of the day.

Although the production team told Caroline to break the order into monthly batches of the same amount, and they would meet the requirements, Caroline protested with the argument $,$ "Why don$$t we just build what we need and use our flexible manufacturing resources to do it$?$ Wouldn$$t that be better?? $$ She asked....

Just then Joseph over heard their conversation discussing the production plan. After hearing the discussion, he told them both $($Caroline and Dina$)$ I need to see the lowest cost option to produce these tanks. "But I don$$t$\text{'}$ want to lose any sales through lack of inventory! Perhaps we should have about $500$ or so as opening stock and see if that keeps the plan in balance. I think it will. I think...." Joseph concluded.

The sales team developed the forecast as requested. Starting in January and ready to be shipped at each month end the delivery plan was as follows: