John Swanson, president of Market Research Inc., has asked you to estimate the coefficients of the model
Y = β0 + β1X1 + β2X21 + β3X2
where Y is the expected sales of office supplies for a large retail distributor of office supplies, X1 is the total disposable income of residents within 5 miles of the store, and X2 is the total number of persons employed in information-based businesses within 5 miles of the store. Recent work by a national consulting firm has concluded that the coefficients in the model must have the following restriction:
β1 + β2 = 2
Describe how you would estimate the model coefficients using least squares.