(i) The maximax decision rule involves choosing the outcome with the best possible result, in this instance choosing the outcome which maximises contribution. The decision-maker would therefore choose a client fee of $180 per day, which could result in a contribution of $1,732,500.
(ii) The maximin decision rule involves choosing the outcome that offers the least unattractive worst outcome, in this instance choosing the outcome which maximises the minimum contribution. The decision-maker would therefore choose a client fee of $200 per day, which has a lowest possible contribution of $1,378,125. This is better than the worst possible outcomes from client fees per day of $180 and $220, which would provide contributions of $1,338,750 and $1,312,500 respectively.
(iii) The minimax regret decision rule involves choosing the outcome that minimises the maximum regret from making the wrong decision, in this instance choosing the outcome which minimises the opportunity lost from making the wrong decision. We can use the calculations performed in (a) to draw up an opportunity loss table.
The minimax regret decision strategy would be to choose a client fee of $200 to minimise the maximum regret at $26,250.
Workings
1 At a variable cost of $95 per day, the best strategy would be a client fee of $200 per day. The opportunity loss from using a fee of $180 would be $(1,378,125 – 1,338,750) = $39,375.
2 The opportunity loss in this case is $(1,378,125 – 1,378,125) = $0.
3 The opportunity loss in this case is $(1,378,125 – 1,312,500) = $65,625.
4 At a variable cost of $85 per day, the best strategy would be a client fee of $200 per day. The opportunity loss from using a fee of $180 would be $(1,509,375 – 1,496,250) = $13,125.
5 The opportunity loss in this case is $(1,509,375 – 1,509,375) = 0.
6 The opportunity loss in this case is $(1,509,375 – 1,417,500) = $91,875.
7 At a variable cost of $70 per day, the best strategy would be a client fee of $180 per day. The opportunity loss from using a fee of $180 would be $(1,732,500 – 1,732,500) = $0.
8 The opportunity loss in this case is $(1,732,500 – 1,706,250) = $26,250.
9 The opportunity loss in this case is $(1,732,500 – 1,575,000) = $157,500.
