Describe the choice variables, objective functions and feasible sets in the following optimization problems: (a) You may go from college to home on foot, by bus or by train. You know with certainty...

Describe the choice variables, objective functions and feasible sets in the following optimization problems: (a) You may go from college to home on foot, by bus or by train. You know with certainty how long it takes by each mode, and what it will cost. The problem is to choose the ‘best’ way of going home. (b) You want to go on a diet which will involves as few calories as possible, subject to a certain minimum, and which will ensure that you consume at least minimum amounts of vitamins. You also cannot exceed your weekly food expenditure budget. You know the price, calorie count and vitamin content of one unit of every foodstuff. There also exists a calorie-free but expensive all-vitamin tablet. How do you choose the ‘best’ diet? (c) A consumer may shop at market A, which is very close to his home, or take a bus ride and shop at market B, where prices are relatively lower. The problem is to choose whether to shop at market A, market B, or both.