Suppose there are two goods (wheat and lamb) and two perfectly divisible fields, K (hilly) and L (flat), each of 100 acres. Output per acre is as follows and requires no labour or capital input.

x=1.5K+5L , y=K+2L

Derive the transformation curve(=production possibility frontier). (Warning : it is not smooth but kinked.)

If Crusoe has u = xy, how should the fields be allocated?

(from Layard, Walters, chapter 1, question 1-5)