please help. thank you

2. (14 points) For this problem, please use a continuous cost function and allow the rm to produce non-integer units of output. Consider a rm with production function: Q = K.6 L3 And which faces a wage of $20/unit and a rental rate on capital of $30/unit. a) Please write the long-run cost function of this rm. b) Please write the equation for the long-run marginal cost function and the long run average cost function of this rm. 0) In the long-run, how much will this rm offer to the market and what are the prots of the rm when the price of output is $100? d) Please write the short-run cost function, the short-run marginal cost inction, and the short- run average cost function of the rm when capital is xed at 32 units. Draw the supply curve of the rm. 6) How much will this rm offer to the market and what are the prots of the rm when the price of output is $100? 1) Please give an intuitive explanation for the differences in your answers for parts c) and e). g) For what value of Q are the short-run cost function and the long-run cost function equal