z ≤ 1/2 (225 - 7y^2)
Let f(y) = 225y - 7y^2
f'(y) = 225 - 14y
f'(y) = 0 gives y = 225/14
f''(y) = -14 < 0
∴ y = 225/14 is point of maxima of f(y).
∴ f(225/14) is maximum value
Maximum value = 225 x 225/14 - 7(225/14)(225/14)
= (225)^2/14 (1 - 1/2)
= (225)^2/28
= (225)^2/4 x 7
Hence, 225y - 7y^2 ≤ (225)^2/4 x 7
∴ z ≤ 1/2 (225 - 7y^2) ≤ (225)^2/ 2 x 4 x 7