DID retailers sell television sets, and they are ordering a single shipment of the Sony XF70 sets to cover demand for the next two months. Demand for this set averages 25 units per month with a standard deviation of 8 units per month (note that this means in a 2-month period demand will average 50 units with a standard deviation of 8*2 = 11.3 units). DID will place an order for immediate delivery, and any units unsold after 2 months will be sold off at half price as the XF70 will be then replaced by a new model. Each set costs 1000 to buy in and currently sells for 1700.

(c) The television set distributor offers DID the option to switch from making a single order to making two orders - one order at the beginning of each month, each with immediate delivery. For DID any sets unsold in the first month can be held over to the following month and then sold at full price. However, DID would incur a storage charge of 10% of the cost of the stock for any unsold sets at the end of the first month. Any sets remaining at the end of the second month will be sold off at half price as before. The distributor will charge a fee of 2000 to provide this service.

If they were to accept this offer, how many sets would DID order for delivery for the first month, in order to maximise their likely profit for that month, assuming they currently have no sets in stock?

(25 marks)

(d) Following on from (c) above, at the end of the first month DID have been left with 4 XF70 sets unsold. How many sets would DID order for immediate delivery for the second month, in order to maximise their likely profit for that month?

Would you recommend that DID take up the option of the monthly order/delivery as opposed to a single order/delivery? Explain fully the justification for your recommendation. (35 marks)