29 A manufacturer buys valves from two suppliers. The quality of the valves from the suppliers is as follows:

PERCENTAGE DEFECTIVE PROBABILITY FOR SUPPLIER A PROBABILITY FOR SUPPLIER B 1 0.60 0.30 3 0.25 0.40 5 0.15 0.30 For example, the probability of getting a batch of valves that are 1% defective from supplier A is 0.60. Because the manufacturer orders 10,000 valves per order, this would mean that there is a 0.6 probability of getting 100 defective valves out of the 10,000 valves if supplier A is used to fill the order. A defective valve can be repaired for 60 cents. Although the quality of supplier B is lower, it will sell an order of 10,000 valves for $37 less than supplier A.

(a) Develop a decision tree to help the manufacturer decide which supplier it should use.

(b) For how much less would supplier B have to sell an order of 10,000 valves than supplier A for the manufacturer to be indifferent between the two suppliers?