Given the production function Q = 9K^1/3L^1/3T^1/3 , where K is capital, L is labor, T is land.

i. Determine the output when K = 1000, L = 27, T = 125.

ii. Estimate KQ , LQ and TQ at (1000, 27, 125).

iii. Using Young's theorem, find all the 2nd partial derivatives in ii.

iv. Given the number of labour increase from 27 to 30, while capital remains at 1000 and land remains at 125. Determine the approximate change in output.