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Question 2b
Cement Co is a company specialising in the manufacture of cement, a product used in the building industry. The company has found that when weather conditions are good, the demand for cement increases since more building work is able to take place. Cement Co is now trying to work out the level of cement production for the coming year in order to maximise profits. The company has received the following estimates about the probable weather conditions and corresponding demand levels for the coming year:
| Weather | Probability | Demand |
|---|---|---|
| Good | 25% | 350,000 bags |
| Average | 45% | 280,000 bags |
| Poor | 30% | 200,000 bags |
Each bag of cement sells for $9 and costs $4 to make. If cement is unsold at the end of the year, it has to be disposed of at a cost of $0·50 per bag. Cement Co has decided to produce at one of the three levels of production to match forecast demand. It now has to decide which level of cement production to select.
Required:
(b) Determine the level of cement production the company should choose, based on the decision rule of maximin. Show your calculations clearly and justify your decision. (2 marks)