Chapter 3.4, Problem 46P

(a)

To determine

To find:

The method in way it is possible for the total cholesterol of the patient to increase but the cholesterol ratio to remain constant if cholesterol ratio is given by the ratio of good cholesterol $G\left(t\right)$ to the total cholesterol $R\left(t\right)=\frac{G\left(t\right)}{T\left(t\right)}$. The safety situation is when the cholesterol ratio is $R\left(t\right)>\frac{1}{5}$.

(b)

To determine

To calculate:

The rate of change of total cholesterol level in the first week of the diet. On January 1, the total cholesterol is $120\raisebox{1ex}{$\text{mg}$}\!\left/ \!\raisebox{-1ex}{$\text{dl}$}\right.$ and the good cholesterol level is $30\raisebox{1ex}{$\text{mg}$}\!\left/ \!\raisebox{-1ex}{$\text{dl}$}\right.$ Although the cholesterol ratio is in safety limit but the doctor prefers that the good cholesterol increases with $40\raisebox{1ex}{$\text{mg}$}\!\left/ \!\raisebox{-1ex}{$\text{dl}$}\right.$. In order to change the diet-plan the good cholesterol needs to change with the rate $1\raisebox{1ex}{$\text{mg}$}\!\left/ \!\raisebox{-1ex}{$\text{dl}$}\right.$. Cholesterol ratio is given by the ratio of good cholesterol $G\left(t\right)$ to the total cholesterol $R\left(t\right)=\frac{G\left(t\right)}{T\left(t\right)}$. The safety situation is when the cholesterol ratio is $R\left(t\right)>\frac{1}{5}$.