Find the max value of C=6x-2y Subject to the following constraints:

x≥0

y≥0

x+2y≤14

4x-y≤20

Graph the equations or solve the system of equations to find the vertices within the shaded region.

x≥0, y≥0 represents the first quadrant.

x + 2y ≤ 14 ⇒ has intercepts (14, 0) and (0, 7).

4x - y ≤ 20; has intercepts (5, 0) and (-20, 0). Disregard (-20, 0) since it is not in Quadrant 1.

x + 2y ≤ 14 and 4x - y ≤ 20 intercept at (6,4).

Now evaluate the value (C) at the intercepts (0, 7), (5, 0), and (6,4). Note: (14, 0) has been disregarded because it is outside of the shaded region.

C = 6x - 2y at (0, 7) ⇒ C = 6 (0) - 2 (7) ⇒ C = 0 - 14 ⇒ C = - 14

C = 6x - 2y at (5, 0) ⇒ C = 6 (5) - 2 (0) ⇒ C = 30 - 0 ⇒ C = 30

C = 6x - 2y at (14, 0) ⇒ C = 6 (6) - 2 (4) ⇒ C = 36 - 8 ⇒ C = 28

The maximum value (C) equals 30

Answer: maximum value is 30