A company is planning to add extra capacity to a plant currently manufacturing 110 000 items per year.
After an accurate sales forecast over the next few years, one is quite sure that the most likely value of the annual demand is 140 000 items and that the MSE is equal to 108.
It is known that the company loses $ 3 for each unit of unused capacity and $ 7 for each unit of unsatisfied demand. How much capacity should the company buy?
(Hint: the forecasting error can be assumed to be normally distributed.)