The demand for a new product at Company B is anticipated to be normally distributed with a mean of 100 and a standard deviation of 50. Each unit costs 75 and the introductory price is to be 125. Any unsold units at the end of the season are unlikely to be very valuable and will be disposed of in a sale for 25 each. It costs 10 to hold a unit in inventory for the entire season

a) How many units should be ordered tomaximise expected profits? Please show your full working.

b) Based on additional market research that Company B performs, they determine that they can increase the price to 150. At the same time, they have made an arrangement with an outlet store that will purchase unsold units for 60 each. Without any calculations, comment on the effect of these changes on the optimal customer service level and the optimal order quantity.

c) What impact would postponement and improved forecasting have on the inventory level for the new product at this company? Why?

d) After two months, the real demand for this new product has been recorded in the following table. Based on this information and the customer service level you calculated in a), what should the optimal order size be? Please show your full working.

Demand (units)	Probability
300	0.058
320	0.077
340	0.115
360	0.173
380	0.173
400	0.154
420	0.115
440	0.096
460	0.038