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On an island economy, Sarah has 40 units of labor to allocate between producing x and...

On an island economy, Sarah has 40 units of labor to allocate between producing x and y. Her utility function is u(x,y) = 2xy. The production functions are x = 5Lx and y = 9(L_y)^0.5 where L_x and L_y are the labor units allocated to sector x and y.
(a.) Find the equation of the PPF and carefully graph it.
(b.) Find Sarah’s optimal consumption pair (x*,y*) and corresponding labor allocation (L_x*,_Ly*).

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