1. Establish a model. Let the sequence c(n) be the total deposits at the beginning of the nth year.

Obviously, the problem is to minimize c(1), that is, to minimize the total amount in the first year, so as to satisfy the maximum payment.

The total deposit consists of 3 parts, namely c(n)=x(n)+0.98y(n)+0.965z(n) (1-1) where x(n), y(n), z(n)

They are the shares of short-term deposits, 6-year Treasury bonds and 13-year Treasury bonds respectively.

In order to unify the expression form, the number of parts of x can be a decimal, and one part is 1 million yuan; the other parts y and z are all integers.

The x, y, and z numbers are the basic independent variables, which determine the investment method and proportion.

The income s(n) at the end of each year is related to the investment in previous years, that is, s(n)=1.04x(n-1)+1.04y(n-6)+1.03z(n-13) (1-2)

And since the income at the end of each year, excluding bonuses, is used as investment at the beginning of the next year, c(n+1)=s(n)-f(n) (1-3) where f(n) is the bonus f distributed at the end of each year

=[10,11,...].

Note that bonuses are guaranteed every year, and the above formula continues to satisfy the condition >=0, that is, s(n)-f(n) >=0 (1-4) 2. Problem simplification Since no bonuses will be generated after the 15th year, so

x(n>16-1)=0 y(n>16-6)=0 (2-1) z(n>16-13)=0 That is, the sequence is finite.

The intermediate variables c and s satisfy formulas (1-1) to (1-3), where n ranges from 1 to 15.

Obviously c(16)=0, c(1) is what is required.

Since f is known, there are five sets of independent variables ***x, y, z, c, and s. The number is 15+13+14+15=57, which satisfies 15+15+14=44 equations.

There is 1 strain variable, namely c(1).

The constraints that need to be satisfied are formula (1-4), and there are ***15 inequalities.

3. Specific solution As can be seen from the previous analysis, this is a typical linear programming problem with constraints.

Therefore, it is recommended to use the lp function in matlab to implement it.

You can check the relevant data for details, so I won’t go into details here.