Homework Answers

A poultry farmer in Lufyanyama has obtained a loan from the Bank to boost his poultry business. He provides you with data to help him optimize the sales. The data is that Old hens can be bought for K2 each but young one cost K5 each. The old hens lay 3 eggs per week and young ones 5 eggs per week, each egg being worth 30ngwee. A hen cost K1 per week to feed. If a person has only K80 to spend on hens, how many of each kind should he buy to get a profit of more than K6 per week assuming that he can’t house more than 20 hens?

Let K be a field and f : Z → K the homomorphism of

integers into K.

a) Show that the kernel of f is a prime ideal. If f is an embedding,

then we say that K has characteristic zero.

b) If kerf f= {0}, show that kerf is generated by a prime number

p. In this case we say that K has characteristic p.