(a) The Alternative Sustenance Company is considering introducing a new franchised product, Wholefood Waffles. Existing ovens now used for making some of the present ?Half-baked? range of products could be used instead for baking the Wholefood Waffles. However, new specialized batch mixing equipment would beneeded. This cannot be purchased, but can be hired from the franchiser in three alternative specifications, for batch sizes of 200, 300 and 600 units respectively.The annual cost of hiring the mixing equipment would be ?5000, ?15 000 and ?21 500 respectively.The ?Half-baked? product, which would be dropped from the range currently earns a contribution of ?90 000 per annum, which it is confidently expected could be continued if the product were retained in the range.The company?s marketing manager considers that, at the market price for Wholefood Waffles of ?0.40 per unit, it is equally probable that the demand for this product would be 600 000 or 1 000 000 units per annum.The company?s production manager has estimated the variable costs per unit of making Wholefood Waffles and the probabilities of those costs being incurred, as follows:

You are required:(i) To draw a decision tree setting out the problem faced by the company;(ii) To show in each of the following three independent situations which size of mixing machine, if any, the company should hire:1. To satisfy a ?maximin? (or ?minimax? criterion);2. To maximize the expected value of contribution per annum;3. To minimize the probability of earning an annual contribution of less than ?100 000.(b) You are required to outline briefly the strengths and limitations of the methods of analysis which you have used in part (a) above.

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200 units 300 units Probability if Probability if 600 units Probability 600 units annual sales annual sales if annual Batch are either are either Probability if size: Cost 600000 or 600 000 or annual sales sales are per unit (pence) 1000000 1000 000 are 600000 1000000 units units units units £0.20 0.1 0.2 0.3 0.5 £0.25 0.1 0.5 0.1 0.2 £0.30 0.6 0.3 0.8 0.3