$(20$ points$)$ Set up a linear program to determine the optimal borrowing strategy for the coming year. The objective is to minimize the total interest payed

during the whole year. Write down variables, objective, and constraints on

paper. Draw a picture to visualize the balance constraints.

$2.(10$ points$)$ To develop intuition, find a $$good$$ solution by inspection to a toy

problem, whose data is given below: This time, make srate equal to zero, but

the objective should be to minimize the total amount borrowed. Write down

your solution.

Month i $1234$

Expenses $101000$

Revenues $001010$