(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 special batch mixing equipment would be needed. 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 ears 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 10.40 per unit, it is equally probable that the demand for this product would be 600 000 or 1000 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: 200 units 300 units Probability Probability if annual if annual 600 units sales are sales are Probability 600 units either either if annual Probability Batch size: 600 000 or 600 000 or sales are if annual Cost per unit 1 000 000 1 000 000 600 000 sales are (pence) units units units 1 000 000 10.20 0.1 0.2 0.3 0.5 10.25 0.1 0.5 0.1 0.2 10.30 0.8 0.3 0.6 0.3 You are required: to draw a decision tree setting out the problem faced by the company. (12 marks to show in each of the following three independent situations which size of mixing machine, if any, the company should hire: to satisfy a 'maximin' for minimax criterion). to maximize the expected value of contribution per annum