A firm has the technology q = z 1 z 2 z 3 where: z 1 , z 2 and z 3 are its inputs, there are non-negative constants , , , and q is its output. (a) Do the isoquants touch the axes? (b) What are the MRTS's between the three products? (c) For what values of the constants is this technology homogeneous? (d) For what values of the constants is this technology homothetic? (e) Suppose the input prices are a, b, c > 0 for the three products. Find the cheapest cost of producing q units of output using only the third input. Find the cheapest cost of producing q units of output using the first two inputs. When is it optimal to not use all the inputs