A news vendor buys a daily paper from a publisher for a unit price of 2.5 and sells it to members of the public for 3.20. Any papers left over at the end of the day are returned to the publisher and for each copy of the daily paper returned the news vendor receives 1.0.

(a) Past experience indicates that the demand from the members of the public for this magazine is expected to have a Normal distribution with mean demand of 120 copies and variance 20 copies. By making use of the standard Normal distribution table (with mean zero and variance one) what would be your advice as to how many copies the news vendor should order from the publisher? (4 marks)

(b) Suppose the news vendor successfully negotiates with the publisher for returned daily papers and recover 1.8 per copy. At the same time, he increases the selling price per copy of the daily paper to 3.70 as he now buys the daily papers from the publisher at a unit price of 2.70. What now would be your advice as to how many copies the news vendor should order from the publisher?

(c) The news vendor also sells packets of mint sweets that he currently orders once every two weeks from a supplier. He pays his supplier 1.25 for each packet and currently sells 520 packets a week. He estimates that the cost associated with making an order are 3.25 and interest rate are currently 0.25% per week. His suppliers offer a quantity discount such that if he and his three other news vendor friends collectively were to order 1,500 packets or more each time, they would get a 10% discount. Also, with this arrangement assume that the interest rate drops to 6% per year. Assume that there are 52 weeks in a year, what advice can you offer the news vendor? (10 marks)

d) The packets of mint sweets are produced by the news vendors supplier on a machine that cost 1,250 to be set up. The supplier has the ability to produce 25,000 packets of mint sweets per week on this machine and interest rates are currently 10% per annum. Producing one packet of mint sweet is estimated to cost 0.4 in labour and 0.35 in materials. Part finished of mint sweets through previous stages of the production process have already cost the (supplier) company 0.25 each. The supplier sells packets of mint sweets to a number of vendors and (on average) this collective order is 2,000 packets per day. Assume that there are 52 weeks in a year, what advice can you offer the supplier in terms of the operation of this machine and the associated total cost per year? (7 marks)