A plant has a production function F(z) = (z1^1/2)*(z2^3/4) . The input price vector is p = ( p1 , p2 ) = (2 , 16).

The output price is p3 = 32. The plant manager instructions are to maximize prot.

a. Show that there is a unique critical point.

b. Draw the level sets and you will see that the critical point is not the maximizer.

c. Is there a maximizer? Hint: Consider the prot with input z = ( , ). For what values of does the

prot increase with ?