The manager of a Cummings engine manufacturing facility has collected some historical data on the monthly demand of hemi-diesel engines (See table 1)

Table 1 Period Monthly Demand January 240 February 150 March 350 April 297 May 497 June 566 July 200 August 450 September 300 October 240 November 300 December 350

The unit cost of an engine is $3000 and there is a 30% interest rate associated with the holding cost. It takes 6 weeks for a replenishment order to be placed. Every time the facility has to setup to make these engines the manager estimates a setup cost of around $250,000. The cost of backorders is about $150,000 per year and the manager is worried about this figure. Demand seems to be normally distributed and the manager would like to determine the following:

What is the annual demand of engines?

What is the economic order quantity?

What is the average demand of engines over the six week period for replenishment?

What is the standard deviation of the sample in table 1 (use the STDEV.S function in excel)

Determine the critical fractile of backorder cost. Use the following formula to determine this G(r^* )= b/(b+h)

What the z score of this critical fractile (Hint use the NORMSINV function in excel)