Apollo has the following utility function:
U(2,z) = x^0.8z^0.2
where x = the quantity consumed of good x and z = the quantity consumed of good z. The unit price of good x, is $5 and the unit price of good z,, is $10. Apollo's income is $200, and he uses it all to consume goods x and z. Calculate the following:
(a) Apollo's optimal consumption of good x is
(b) Apollo's optimal consumption of good z is