Construct an improving direction from the gradient of each objective function at the point indicated.

(a) max 3w1 - 2w2 + w4 at w = 12, 0, 5, 12

(b) min -4w2 + 5w3 - w4, at w = 12, 2, 1, 02

(c) min 1w1 + 222 - w1w2 at w = 13, 22

(d) max -4w1 + 9w2 + 21w222 at w = 111, 22