Dear Student
Utility analysis - It is based on the belief that consumer can measure the level of satisfaction that he/she derive from consuming certain amount of goods , that can be measured in term of "utils".
Optimal choice- In the budget set there are certain utilisation bundles given and consumer can pick any set that can gave them maximum satisfaction at any point is optimal choice.Such as there are various combination of chips and Pepsi is given that a person can get in Rs 100. Consumer can pick any one from them that gave maximum satisfaction to them.
Regards