Please answer in depth & explain all parts.

3. (35 points). A rm uses labordenoted by Land capitaldenoted by Kto 2 I produce turnips according to the following production function: q = LEKE . The price of labor and capital is $32 and $2, respectively. a) What are the returns-to-scale properties of the production technology? You must prove your answer. b) Derive the rm's demand for labor and capital as a function of the quantity of turnips, q. c) Derive the lm's total cost of production as a function of the quantity of turnips, q. d) Derive the rm's marginal and average cost of production as a mction of the quantity of turnips, g. e) Explain why the rm's cost functions look the way they look