Mickey is considering buying a tape recorder. His utility function is U(x, y, z) = x + f(y)z^.5, where x is the amount of money he spends on other goods, y is the number of tape recorders he buys, and z is the number of tapes he buys. Let f(y) = 0 if y < 1 and f(y) = 8 if y is greater than or equal to 1. The price of tape recorders is $20, the price of tapes is $1, and Mickey can easily afford to buy a tape recorder and several tapes. Will he buy a tape recorder?

Why is the answer he should not buy a tape recorder?

Can you please show the workings?