economics question

Consider an economy with with two inputs capital (K) and labor (L) with total endowments K=10 and L=20. Suppose that capital and labor can be used to produce two according to the following equations: q1=K1(L1)2 and q2=2K2+L2

1) The problem that solves for the Lerner efficient allocations and the production possibility frontier for this economy is:

2) The Interior Lerner efficient input allocations satisfy:

3) Are there any boundary Lerner efficient input allocations? If so find them:

4) Find the production possibility frontier for this economy:

5) Sketch the Lerner efficient allocations in an Edgeworth box: