You manage Dirt Diggers, an excavating firm that excavates roadside ditches for laying drainpipes. Its output follows the production function: Q = 10L -.1L2 where L denotes labor hours and Q the length of the ditch in meters. You can hire labor at the going wage rate of $12 per hour. As the manager of DD you want to earn as high a profit as possible.

(a) You have received an offer to excavate 250 meters for a lump sum payment of $500. Should you accept the offer ? Explain with appropriate calculations.

(b) Suppose that instead of the previous offer, you are now offered as much or as little excavation work at a price of $2.00 per meter dug. Should you accept the offer ? Why or why not ? If you accept the offer calculate resulting profit. Also, calculate the optimal level of output (meter dug) and the level of labor usage.