An ice cream manufacturer sells soft scoop ice cream in special pressurised containers and is planning production for the summer, which is the peak period. The company wishes to ensure that it has the best quantity of containers on hand: too few and sales will be lost; too many and the surplus will have to be stored over the winter at a substantial cost. The containers can only be purchased in lots of 500.

The following table shows the estimated lost contributions for various ordering patterns:

Based on past data, the probabilities of the different types of weather are:
Poor : 0.3 Fair : 0.4 Good : 0.2 Very good : 0.1 The firm has obtained a copy of the long-range weather forecast for the summer which indicates that there will be good summer, but past experience states that the forecasts are not 100% accurate, as follows:
P(forecast good but weather poor)= 0.3 P(forecast good but weather fair)= 0.4 P(forecast good and weather good)= 0.7 P(forecast good but weather ve,y good) = 0.2 You are required

(a) to calculate the number of containers that should be purchased based on past data only (i.e. ignore the forecast);

(b) to calculate whether the decision in

(a) would need to be altered if the forecast is taken into account;

(c) to explain any changes made in the purchase decision as a result of comparing your answers to

(a) and

(b) above.

Transcribed Image Text:

Number of New Containers Bought 0 500 1,000 1,500 30 2250 2505 Poor summers-low sales Fair summer-reasonable sales Good summer-good sales Very good summer-very high sales 0528 15 20 30 2022 25