The manufacture of a certain type of electronic board consists of four steps: tinning, forming,

insertion, and solder. After the forming step, 5% of the parts must be re-tinned; after the

insertion step, 20% of the parts are bad and must be scrapped; and after the solder step, 30%

of the parts must be returned to insertion, 10% must be scrapped, and the remaining ones are

stored in the "ready to ship" area. We assume that when a part is returned to a processing

step, it is treated like any other part entering the step.

(a) Model this process as a Markov chain and give its transition matrix.

(b) What is the fraction of parts that end up scrapped?

(c) How many boards should we start with if the goal is to have the expected number of boards that finish in the good category equal to at least 100?