Dirt Diggers (DD) is an excavating firm that excavates roadside ditches for laying drainpipe. Its output follows the following production function: O = 20L - .1L2 where L denotes labor hours and Q the length of the ditch in feet. DD hires labor at the going wage rate of $24 per hours. DD's fixed cost is $800. (a) DD has received an offer to excavate 1000 ft. for a lump sum price of $3000. Should it accept the offer? Explain with appropriate calculations. (6 points) (Hint: Determine the labor hours requirement to for the excavation.) (b) Suppose instead of the previous offer DD is offered as much or as little excavation work at a price of $3.00 per ft. dug. Should it accept the offer? If it does, calculate its profit and the optimal (profit maximizing) output (ft. dug) and labor usage.