Curve Fitting with Constraints. A bank’s economist has been interested in developing a production function for the bank. The model recognizes three explanatory variables, which are measures of resources available to the bank. These are Labor Hours, Operating Expenses, and Capital Expenses. The response variable, which measures output activity, is a weighted average of the transactions processed by all departments in the course of a month. The economist’s model takes the form:

Because the fitted curve is a production function, it represents the ideal output level that could be achieved for any choice of inputs. Thus, the notion is to fit the model to actual data as well as possible, subject to the requirement that the predicted value be at least as large as the observed value for each combination of inputs in the data set.

a. What are the best-fitting values of a₀, a₁, a₂, and a₃?
b. Using the model determined in part (a), what ideal output is predicted for Branch 2? for Branch 4?

Transcribed Image Text:

42 43 Q=a0x¹x²x3