Linear regression

  1. (POINTS: 20) Consider the function f (x, y) =

    xy.
    (a) (Points: 10) Draw a xy-diagram and identify the following region:
    x ≥ 0 and y ≥ 0
    x+9y ≤ 36
    Be precise in your drawing, identifying all relevant elements.

(b) (Points: 7) Draw the level curve f (x, y) = 6 in your diagram above.
Hint: You can think of the level curve as y = y(x), that is, y as a function of x.

(c) (Points: 3) What is the point the level curve intercept the region identified in item (a)?
Hint: The level curve is tangent to the equation x+9y = 36.

Sample Solution