The Production of microchips is given by the Cobb-Douglas function P=4000K^0.3 * L^0.7. K represents capital expenditure (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.

b) If the company is upgrading machinery, increasing capital expenditure $1.8 million per month , allowing them to decrease labor costs by 2,000-hours per month, what is the rate of change in production?

c) If production is to be kept constant at the level P(10,30)=4000*10^0.3 *40^0.7=86307, what would be the expected change in labor-hours per month if capital expenditures are decreased by $2 million per month?