A manufacturer of LEDs tests its product in batches of size n . Suppose that the

Question

A manufacturer of LEDs tests its product in batches of size n. Suppose that the cost of producing each item is 0.30 dollars, and suppose that the cost of each test is 35 dollars (per batch). Suppose that the probability of one LED being faulty is p=0.002. Suppose also that the whole test batch is discarded if one LED in the batch is faulty (and that if the test is passed then all the LEDs can be sold).

a) Calculate the expected number of LEDs that are ready for sale, from a batch of size n using this testing scheme.

b) Calculate the total cost of producing and testing LEDs in the batch.

c) Calculate the cost per item for each of the LEDs that is ready for sale.

Explanation / Answer

as the test will fail 0.002 proprtion of batches and pasess (1-0.002=0.998) proportion of batches.

therefore expected number of LEDs that are ready for sale, from a batch of size n =0.998n

b) total cost =production cost+testing cost) =0.30n+35 dollars

c) cost per item for each of the LEDs that is ready for sale =(0.30n+35)/0.998 =(1000/998)(0.30n+35)

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