11.90 Productivity has been defined as the relationship between inputs and outputs of a productive system.

In order to manage a system’s productivity, it is necessary to measure it. Productivity is typically measured by dividing a measure of system out put by a measure of the inputs to the system.

Some examples of productivity measures are sales/salespeople, yards of carpet laid/number of carpet layers, shipments. [(direct labor)  (indirect labor)  (materials)]. Notice that productivity can be improved either by producing greater output with the same inputs or by producing the same out-

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a = 0.05

+ b4x1x2 + b5x21 x2 E(Y ) = b0 + b1x1 + b2x 21

+ b3x2 put with fewer inputs. In manufacturing operations, productivity ratios like the third example above generally vary with the volume of output produced.The production data in Table 11.8 were collected for a random sample of months for the three regional plants of a particular manufacturing firm. Each plant manufactures the same product.
a Construct a scatterplot for these data. Plot the North-plant data using dots, the Southplant data using small circles, and the Westplant data using small triangles.
b Visually fit each plant’s response curve to the scatterplot.
c Based on the results of part (b), propose a second-order regression model that could be used to estimate the relationship between productivity and volume for the three plants.
d Fit the model you proposed in part

(c) to the data.
e Do the data provide sufficient evidence to conclude that the productivity response curves for the three plants differ? Test by using .
f Do the data provide sufficient evidence to conclude that your second-order model contributed more information for the prediction of productivity than does a first-order model?
Test by using .
g Next month, 890 units are scheduled to be produced at the West plant. Use the model you developed in part

(d) to predict next month’s productivity ratio at the West plant.