Question

Problem 2.1, Dssigning a daily routine for maximizing life span Given: The longest life span ofan average human has been found to be around·10 years. This is revealed to be strongly dependent on the amount of food intake along with the amount of exercise executed. Let Y be the life span in years, Xi, the number of hours of exercise per week, and X, the kilogram of food intake per week. Find: Y -f(X, X2) which gives a maximum Y of around 110 years, and that the corresponding values of X, and X2 are somewhat realistic. Include nice plots showing the variation of Y with respect to X, and X2. List two other key factors which probably should also be included.

Answer 1

The life span of years Y = f(X1, X2), where X1 = number of hours of exercise per week, X2 = the kilogram of food intake per week.

To see the changes of Y due to any change in X1 will be,

dY/dX1 = df(X1,X2)/dX1

Similarly for X2,

dY/dX2 = df(X1,X2)/dX2.

If X1 increases at an excessive level but not X2 even that will hamper the life span as too much exercise but not enough food to eat will not help one to survive. Again, an excessive increase of X2 but X1 will again hamper the life span. Too much food but not enough exercise will again not help one to survive for long.

The two other key factors which probably should be included are : pollution and psychological factor. The first one, pollution includes the surrounding pollution, such as air pollution, water pollution,etc. Due to excessive air pollution, the air that we breath gets polluted, thus this will affect the survival of human lives. Again, psychological factor of a human being has become very important nowadays. People suffering from depression, loneliness has increased, thus these things affects the welfare of a person,thereby affecting the human life span. One tends to commit suicide while he/she is suffering from depression, thus that decreases the life span of human beings. So these are the two other important factors which should be also considered .