A small company finds itself in the position of having to complete a contract for a large customer or pay high financial penalties for failing to deliver. The firm finds itself with a problem. The stocks of one particular component used to assemble the product have been exhausted and the contract cannot be completed. The company has contacted a number of possible local suppliers of this component. The company needs some 10 000 units of the component, which cost £1 each. The quality of the component is very variable, however, and in the past the company has found that 55 per cent of components are acceptable, 30 per cent are of poor quality and the remainder are sub-standard. Poor components can be improved to standard at a cost of 25p per unit while sub-standard components can be rectified at a cost of £1 per unit.

Because of the short timescale for completion of the contract, the company has decided to visit each supplier in turn. A small sample of the component will be inspected and if the components look acceptable, 10 000 will be purchased from that supplier. If the first supplier’s sample is not acceptable the company will inspect a sample from the second supplier, and so on. If, however, the company gets to the fourth and final supplier, it will have to purchase all 10 000 items from this supplier regardless of quality.

Construct a decision tree for this problem and evaluate the likely financial consequences for the company of its situation.