Changes in productivity according to the two measures

Question

Question 1. A company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts.  Prior to buying the new equipment, the company used five workers, who produced an average of 80 carts per hour.  Labor cost was $10/hour and machine cost was $40/hour.  With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $10/hour while output increased by four carts per hour.

a. Compute labor productivity under each system.  Use carts per worker hour as the measure of labor productivity.

b. Compute the total productivity under each system.  Use carts per dollar cost (labor plus equipment) as the measure.

c. Comment on the changes in productivity according to the two measures, and on which one you believe is the more pertinent in this situation? 

Question 2. The quarterly data presented here show the number of appliances (in thousands) returned to a particular manufacturer for warranty service over the past five years.

YEAR                                                RETURNS (in 1000 units) 

2002

            1^st quarter                                1.2

            2^nd quarter                               0.8

            3^rd quarter                                0.6

            4^th quarter                                1.1

2003

            1^st quarter                                1.7

            2^nd quarter                               1.2

            3^rd quarter                                1.0

            4^th quarter                                1.5

2004

            1^st quarter                                2.5

            2^nd quarter                               2.3

            3^rd quarter                                2.2

            4^th quarter                                2.4

2005   

1^st quarter                                           2.6

            2^nd quarter                               2.2

            3^rd quarter                                1.9

            4^th quarter                                2.5

2006   

1^st quarter                                           2.9

            2^nd quarter                               2.5

            3^rd quarter                                2.2

            4^th quarter                                3.0

a. Do the data exhibit any patterns? Please explain.

b. Use an appropriate exponential smoothing forecasting procedure to produce forecasts for the first, second, third and fourth quarters of 2007. Please choose the values of  the exponential smoothing constant(s) in such a way that the mean squared error is minimized

c. How would the company use these forecasts?