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  ALL FIVE questions are compulsory and MUST be attempted

1    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. Last year, the weather was so good, and the demand for cement was so great, that Cement Co was unable to meet demand. Cement Co is now trying to work out the level of cement production for the coming year in order to maximise profits. The company doesn’t want to miss out on the opportunity to earn large profits by running out of cement again. However, it doesn’t want to be left with large quantities of the product unsold at the end of the year, since it deteriorates quickly and then has to be disposed of. 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:

(a)  Construct a pay off table to show all the possible profit outcomes.                                    

(b)  Decide the level of cement production the company should choose, based on the following decision rules:

(i)Maximin

(ii) Maximax

(iii）Expected value

You must justify your decision under each rule, showing all necessary calculations.

(c)  Describe the ‘maximin’ and ‘expected value’ decision rules, explaining when they might be used and the attitudes of the decision makers who might use them.