Suppose the true relationship between E(y) and the quantitative independent variables x₁ and x₂ is described by the following first-order model:

E(y) = 4 - x₁ + 2x₂

a. Describe the corresponding response surface.

b. Plot the contour lines of the response surface for x₁ = 2, 3, 4,where 0 ≤ x₂ ≤ 5.

c. Plot the contour lines of the response surface for x₂ = 2, 3, 4,where 0 ≤ x₁ ≤ 5.

d. Use the contour lines you plotted in parts b and c to explain how changes in the settings of x₁ and x₂ affect E(y).

e. Use your graph from part b to determine how much E(y) changes when x1 is changed from 4 to 2 and x₂ is simultaneously changed from 1 to 2.