A Gas company produces gas leak detectors in batches of 200 and clients will reject a batch if it contains more than two faulty detectors. The manufacturing process produces batches that conform to this standard 90% of the time. The gas company makes a profit of $12000 when a client accepts a batch of detectors and losses $10000 when a customer rejects a batch.Before releasing a batch of gas leak detectors to a client, The gas leak detector company can choose to confirm or test the batch.

Confirmed means that a batch are never faulty and replacing what's faulty before sending to the client to make the client always accept. It cost $4000.

Testing isnt perfect and has 2 possiblties. either meets the client requirement or doesn't meet it. ( 0.75 & 0.9 respectively). It cost $200 and the gas company can do 2 test a batch.

Using given information answer the following.

1. Model this situation as a sequential sampling problem and find the functional equations for the problem.

2. Use the model from (b) to determine a testing policy that maximises the gas company expected profit.

3. Assume that the gas company produces 30,000 batches of detectors per year. For the policy determined in (c), calculate the expected number of batches that are confirmed before being released to client per year.

4. Calculate the risk profile for the policy determined in (c).