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Suppose the production function for some firm during a particular period can be represented by = (, ) = 600 2 2 3 3 . Suppose capital in the short run is fixed at 10 a) Derive the short run production function. b) Derive the marginal product of labour function. c) Derive average product of labour equation. d) Solve for the quantity of labour where diminishing marginal returns of labour set in. e) Solve for the quantity of labour that maximizes output. f) Calculate the maximum output. g) Solve for the units of labour which maximizes average product of labour. h) Prove that at the amount of labour (in g above) the value for average product is equal to marginal product of labour.