On an island economy, Lanai has 80 units of labor, and can produce x using x = 0.5L_x, and y using y = 0.25L_y, where L_x and L_y are labor for sectors x and y. The equation of the PPF is ____, and if Lanai only likes to consume x, she will produce x = ____.

A: 2x + 4y = 80; 40 B:2x + 4y = 80; 20 C:6x + 2y = 120; 40 D:6x + 2y = 120; 20

Mr. Oligarch has a utility function u(x,y) = xy and an endowment of 86 units of labor. Productions functions are x = 0.25L_x and y = 0.2L_y. Find the optimal basket (x*,y*) for Mr. Oligarch in this economy.

A: (12.55, 7.16) B:(10.75, 8.6) C: (8.05, 9.3) D:(6.15, 12.28)

please answer both are question correct