1.A consumer has the following utility function U(x,y,z)=x+y+z . He must maximise his utility subject to his budget constraint m is greater and equal to pxX +pyY+pzZand non-negativity constraints x.y and z aregreater and equal to 0.

a.Write out the Lagrangian for this maximization problem

b.Write the first order conditions for this problem.

c.Find the optimal values of consumption of x, y and z conditional on values of the exogenous variables(px,py,pz,m) . Clearly state which of the constraints are binding in each case.