Robinson has a utility function U=lnx+4lny-L   where x and y are consumption goods and L is labor supply. Output on his South Pacific island lies in the production set Y={ (x,y,l) , x^ 2+y^2<=2L .
(a) solve for utility maximizing choice of input and output.
(b)suppose you are asked to manage the firms . Robinson instructs you to maxmize profit. Assuming that you act as a price taker, which of the following price-wage vectors would lead you to make the same choice as your answer in part (a)\
1. (1,3,1)     2. ( 1,2,1,)    3.(1,1,1)
(c) what profit would the firm make ?
(d) discuss carefylly whether there is a walrasian (price takeing) equilibrium for the robinsion crusoe economy.

哪为高人能指点下啊 ，在三种产品存在的情况下 怎么效用最大话呢？