2. The Production of microchips is given by the Cobb-Douglas function 0.3 0.7 P K L  4000 . K represents capital expenditures(in $ millions) and L represents labor costs(in 1000-hour units). Current costs are $10 million in capital costs and 30,000-hours in labor. a) Find the derivative with respect to time, t (in months), using Implicit techniques. 9pts b) If the company is upgrading machinery, increasing capital expenditures $1.8million per month, allowing them to decrease labor costs by 2,000-hours per month, what is the rate of change in production? 8pts c) If production is to be kept constant at the level 0.3 0.7 P(10,30) 4000 10 30 86307     , what would be the expected change in labor-h