Please provide detailed solutions to the following problems

1) A time study of a job produced the following: average cycle time = 2.25 minutes, performance rating = 1.05. Allowances are 12 percent of the workday (420 minutes). Determine the standard time for this job.

2) An initial time study resulted in an average observed time of 1.4 minutes per cycle, and a standard deviation of .5 minutes per cycle. The performance rating was 1.05. What sample size, including the observations in the initial study, would be necessary to have a confidence of 98 percent that the observed time was within 2 percent of the true value?

3) HEC's product (hydrogen fueled engine) under development took 160 hours for the production of its 2nd unit and 128 hours for its 4th unit.

a) What is the learning curve?

b) How much time did the first unit take?

c) How much time would the production of the 10th unit take?

4) GMP Manufacturing is considering bidding on a small order of 8 units. Based on similar products that they have made in the past, they believe that the first unit will take 300 labor hours. They also believe that there will be an 85% learning curve. How many hours of labor should GMP include for its bid?