How to avoid using linear programming to solve this investment problem?

Hello, everyone. I have an investment question. The questions are as follows.

Now you have a certain amount of initial cash in your hand and need to expand its amount by investing. The bank you invest in offers several different levels of investment packages for you to choose from, but you will need to comply with the following rules set by the bank when buying and selling:

(1) The purchase and sale of each package is carried out according to the whole package, that is, the package you trade each time can only be the whole share;

(2) There is no limit to the number of copies purchased for each package, but there is a limit to the total number of copies purchased for all packages;

(3) The price of the package is the same as when it is bought;

(4) The sale and purchase of packages is concentrated on the first and last day of each month;

(5) The package purchased will generate a fixed profit in the middle of the month;

(6) You can only purchase the next level of package when you hold at least one package of the previous level, and the purchase of the first level package is not restricted;

Now from January 1 of the first year to December 31 of the 10th year, you need to invest with an initial cash of 30,000 yuan to find an optimal investment solution to maximize your final return.

Supplement: As the level continues to rise, the transaction price of a single package continues to rise, as does the fixed profit generated each month.

I know that linear programming can certainly solve this problem, but when the time becomes longer, the complexity of the problem increases greatly. Is there a way to solve this problem without linear programming?

The level of the package, the corresponding price (unit: USD 10000) and the monthly profit (unit: USD) are shown in the figure below.

[Alan Weiss]

This looks like a homework problem. Please show us what you have done to try to answer the assignment, and then ask a question about the particular difficulty you are having.

Alan Weiss

MATLAB mathematical toolbox documentation

[培国 原]

clc,clear,close all
Grade=readmatrix("新建 Microsoft Excel 工作表.xlsx","Range",'A2:A32');
Price=readmatrix("新建 Microsoft Excel 工作表.xlsx","Range",'B2:B32')*1e4;
Profit=readmatrix("新建 Microsoft Excel 工作表.xlsx","Range",'C2:C32');
Time=120;M0=30000;Num=40;much=length(Grade);
prob=optimproblem("ObjectiveSense","maximize");
x=optimvar('x',much,Time,'Type',"integer","LowerBound",0);
m=optimvar('m',1,Time,'Type',"integer","LowerBound",0);
prob.Objective=m(end);
prob.Constraints.con1=m(2:end)-m(1:end-1)-Profit'*x(:,2:end)==0;
prob.Constraints.con2=m(1)-M0+Profit'*x(:,1)==0;
prob.Constraints.con3=M0-Price'*x(:,1)>=0;
prob.Constraints.con4=m(1:end-1)-Price'*x(:,2:end)>=0;
prob.Constraints.con5=sum(x,1)<=Num;
con6=optimconstr(much,Time);
for i=2:much
    for j=2:Time
        con6(i,j)=x(i,j)-Num*x(i-1,j-1)<=0;
    end
end
prob.Constraints.con6=con6;
[sol,fval,flag,out]=solve(prob);

[培国 原]

Due to personal equipment reasons, I am not particularly inclined to use linear programming to solve this problem, so I would like to ask whether there is a nonlinear programming method to solve this problem

[培国 原]

This problem is abstracted and adapted from a tower defense game that few people pay attention to

[Abolfazl Chaman Motlagh]

By linear programming you mean THE "linear programming" means the algorithm for linear cost function and linear constraints. or you mean the "Simplex" method? because for example you can solve the linear problem with interior points algorithm and it is more efficient in large number of parameters and variables than simplex.

[Matt J]

Due to personal equipment reasons, I am not particularly inclined to use linear programming to solve this problem.

What equipment do you have, so that we know how to target our advice?