1.You own a company that digs trenches for utility and telephone companies that need to install their pipes and cables underground.To dig your trenches, you use both labor with shovels (L) and/or mechanical excavators (K).Your production function for digging trenches is q = 3L + 10K, where "q" is number of linear feet of trench dug up, "L" is number of labor hours and "K" is number of hours your mechanical excavators are operated.You pay your labor who dig the trenches $13 an hour.It cost you $50 an hour to operate a mechanical excavator, with the cost covering all cost including operator time, fuel used, and lease cost on the excavator.You have just received an order from AT&T to dig 3,000 feet of trench for AT&T to install optic cable.

a.How many labor hours (L) and hours of mechanical excavators (K) do you use to produce the 3,000 feet of trench? (3 points)

b.Just before your start your AT&T job, the manufacturer of the excavators comes out with a new model that is 30% more productive than the excavators you are using.Since it will cost you the same $50 per hour operating cost for the new model excavators, you decide to replace your current excavators with the new ones.You can replace them in time to use on the AT&T job.How many labor hours (L) and hours of the new mechanical excavators (K) do you now use to produce the 3,000 feet of trench? (2 points)