A company produces items at a cost to them of 110E per item. On top of that there are fixed costs of 700,000E. The expected number of sales is modelled using the function 70,000 - 200p where p Euro is the shelf-price of an item (in the shop). Determine the optimal price per item p (in the shop) that will maximise the profit. Also, briefly comment on the opinion that the function describing the expected number of sales ought to be S-shaped