Consider the linear optimization problem with inputs x y

Question

Consider the linear optimization problem with inputs x, y and constraints

x + 2y ≤ 10

x + y ≤ 7

x ≤ 6

x ≥ -1

y ≥ 0

and a profit function

f(x, y) = 2x - 4y

(a) Draw the feasible region C for this optimization problem in the x, y-plane. (Hint: Allow space on the x-axis from -5 to 12 and on the y-axis from -3 to 8.)

(b) Find the vertices of C

(c) Find the maximum value and the minimum value of the profit function f(x, y) among all (x, y) ∈ C.