9. [Gradients and Approximations] [C] [S] A company wants to produce widgets. The CobbDouglas produc tion function for the company is PlL: K} = (0.05)L2/3K1/3, where L how much money is spent to pay labor and K is how much money is spent on capital, both in millions of dollars, and P is the number of widgets produced in a year, in millions of widgets. Currently, the company spends 2.? millions dollars on labor and 8 hundredthousand dollars on capital. (a) How many widgets will be made this year? (b) If we spend $75,000 more in labor and $50,000 more in capital, then give a linear approximation for how much we expect production to change? {c} If we want production to increase the most, should we invest more in capital or labor? In what ratio?