Question 1117091
I already answered this question recently (hopefully from a student unknown to you) as question number 1116231.
A copy of my previous answer {{{red"(edited)"}}} is attached below.
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THE PROBLEM:
If I understand the story, there are 3 different investments being considered:
A) a financial stocks investment that returns 3%,
B) a slightly more risky retail company investment that returns 5%, and 
C) a new, startup company that is expected to return 12%, but is the riskiest choice.
Because of the risk, you want to invest no more than 30,000,000, pesos in option C),
and to balance risk between options A) and B),you want to invest at least 3 more times in A) than in B).
 
THE EXPECTED ANSWER:
1. The variables that will be used
{{{x}}}= amount invested in B), the retail company, in pesos.
{{{y}}}= amount invested in A), the financial stocks, in pesos.
2. The optimization function that will be used
{{{P(x,y)}}}= the profit returned by the mix of investments.
To figure out what the function "formula" is,
you multiply each amount invested times the percentage return expected (as a decimal),
and add the results.
{{{"5%"=5/100=0.05}}} of {{{x}}} pesos is {{{0.05x}}} pesos.
{{{"3%"=3/100=0.03}}} of {{{y}}} pesos is {{{0.03y}}} pesos.
The amount to be invested on C), the "startup arm" is
{{{"100,000,000"-x-y}}} , and the {{{"12%"=12/100=0.12}}} profit expected from that investment is
{{{0.12("100,000,000"-x-y)="12,000,000"-0.12x-0.12y}}} .
So {{{P(x,y)=0.05x+0.03y+"12,000,000"-0.12x-0.12y}}} , which simplifies to
{{{highlight(P(x,y)="12,000,000"-0.07x-0.09y)}}}
2a. What kind of optimization will be done: minimization or maximization?
Do we want to maximize profit or to keep it to a minimum?
We want {{{highlight(maximization)}}} , of course.
3. The constraints that the linear program will be subjected to
We do not invest negative amounts, and that gives us the constraints
{{{highlight(x>=0)}}} ,
{{{highlight(y>=0)}}} , and
{{{"100,000,000"-x-y>=0}}} <--> {{{highlight(red(x+y<="100,000,000"))}}}
We are told not to invest more than 30,000,000 in risky option C, so
{{{"100,000,000"-x-y<="30,000,000"}}} <--> {{{highlight(green(x+y>="70,000,000"))}}}
is another "constraint".
The advice to invest "at least 3 times more in the financial stocks than the retail arm" translates into the constraint
{{{highlight(blue(y>=3x))}}} .
4. Although you did not ask, you would graph the "feasible region" determined by your constraints as the quadrilateral ABCD below.
{{{drawing(400,400,-20000000,120000000,-20000000,120000000,
line(-30000000,0,120000000,0),arrow(100000000,0,120000000,0),
line(0,-30000000,0,120000000),arrow(0,100000000,0,120000000),
line(25000000,-2000000,25000000,2000000),
line(50000000,-2000000,50000000,2000000),
line(75000000,-2000000,75000000,2000000),
line(100000000,-2000000,100000000,2000000),
line(-2000000,25000000,2000000,25000000),
line(-2000000,50000000,2000000,50000000),
line(-2000000,75000000,2000000,75000000),
line(-2000000,100000000,2000000,100000000),
locate(85000000,-2500000,"100,000,000"),
locate(-20000000,105000000,"100,000,000"),
red(line(100000000,0,0,100000000)),
green(line(70000000,0,0,70000000)),
blue(line(0,0,50000000,150000000)),
locate(-4000000,72000000,D),locate(-4000000,100000000,C),
locate(17000000,50000000,A),locate(27000000,78000000,B),
locate(118000000,0,x),locate(2000000,120000000,y)
)}}}
The blue line is {{{blue(y=3x)}}} . The points on that line and those above the line satisfy constraint {{{blue(y>=3x)}}} .
The red line, with equation {{{red(x+y="100,000,000")}}} {{{red(added)}}} ,
and the points below it satisfy {{{red(x+y<="100,000,000")}}} .
The green line, with equation {{{green(x+y="70,000,000")}}} {{{red(added)}}}  and the points above it satisfy {{{green(x+y>="70,000,000")}}} .
The points in the first quadrant, including the origin and the positive x- and y-axes satisfy the constraints {{{x>=0}}} and {{{y>=0}}} .
The points inside and on the border of quadrilateral ABCD satisfy all constraints and are the feasible region.
5. Although you did not ask, each profit value of {{{P(x,y)=K}}} graphs as a staring line.
For example,
{{{"5,700,000"="12,000,000"-0.07x-0.09y}}} <--> {{{0.07x+0.09y="6,300,000"}}} and
{{{"8,850,000"="12,000,000"-0.07x-0.09y}}} <--> {{{0.07x+0.09y="3,150,000"}}}
graph as the black slanted lines shown below.
{{{drawing(400,400,-20000000,120000000,-20000000,120000000,
line(-30000000,0,120000000,0),arrow(100000000,0,120000000,0),
line(0,-30000000,0,120000000),arrow(0,100000000,0,120000000),
line(25000000,-2000000,25000000,2000000),
line(50000000,-2000000,50000000,2000000),
line(75000000,-2000000,75000000,2000000),
line(100000000,-2000000,100000000,2000000),
line(-2000000,25000000,2000000,25000000),
line(-2000000,50000000,2000000,50000000),
line(-2000000,75000000,2000000,75000000),
line(-2000000,100000000,2000000,100000000),
locate(85000000,-2500000,"100,000,000"),
locate(-20000000,105000000,"100,000,000"),
red(line(100000000,0,0,100000000)),
green(line(70000000,0,0,70000000)),
blue(line(0,0,50000000,150000000)),
locate(-4000000,72000000,D),locate(-4000000,100000000,C),
locate(17000000,50000000,A),locate(27000000,78000000,B),
locate(118000000,0,x),locate(2000000,120000000,y),
line(0,70000000,90000000,0),line(0,35000000,45000000,0),
locate(38000000,12000000,0.07x+0.09y="3,150,000"),
locate(35000000,50000000,0.07x+0.09y="6,300,000")
)}}}
All such lines have the same {{{-7/9}}} slope, so they are parallel,
with a profit of {{{"6,300,000"}}} pesos represented by the upper line shown, and a profit of {{{"8,850,000"}}} pesos represented by the lower line.
As the profit increases the line slides down, parallel to itself,
but the lower line is outside the feasible region,
failing some of the constraints.
It is obvious that in this case, the maximum profit will happen at point A,
as a fifth grader could tell you without much math.
With this type of problem, the lines for constant optimum value slide until they get to a corner or an edge of the feasible region.
That is why your teacher will tell you to calculate the value of the optimization function at all corners of the feasible region to find the optimum value of the function and the conditions (x and y) that produce that optimum value.
{{{red("EDIT")}}} (added calculations):
For point {{{B}}} , the coordinates are {{{system(x="25,000,000",y="75,000,000")}}} , the solution to
{{{system(blue(y=3x),red(x+y="100,000,000"))}}} .
That means investing {{{"25,000,000"}}} pesos on the retail company,
{{{"75,000,000"}}} pesos on financial stocks, and nothing on the startup.
and the value of the optimization function is
{{{P("25,000,000","25,000,000")="12,000,000"-0.07*"25,000,000"-0.09*"25,000,000"="3,500,000")}}} ,
meaning a profit of {{{"3,500,000"}}} pesos.
For point {{{A}}} , the coordinates are {{{system(x="17,500,000",y="52,500,000")}}} , the solution to
{{{system(blue(y=3x),green(x+y="70,000,000"))}}} .
That means investing {{{"17,500,000"}}} pesos on the retail company,
{{{"52,500,000"}}} pesos on financial stocks, and {{{"30,000,000"}}}  on the startup.
and the value of the optimization function is
{{{P("17,500,000","52,500,000")="12,000,000"-0.07*"17,500,000"-0.09*"52,500,000"="6,050,000")}}} .
If you choose point {{{C}}} , with {{{x=0}}} , {{{y="100,000,000"}}} ,
you are investing all {{{"100,000,000"}}} on financial stocks,
for a profit of {{{P(0,"100,000,000")="12,000,000"-0.07*0-0.09*"100,000,000"="3,000,000")}}} pesos.
If you choose point {{{D}}} , with {{{x=0}}} , {{{y="70,000,000"}}} ,
you are investing {{{"70,000,000"}}} pesos on financial stocks,
and {{{"70,000,000"}}} pesos on the startup,
for a profit of {{{P(0,"100,000,000")="12,000,000"-0.07*0-0.09*"70,000,000"="5,700,000")}}} pesos.
 
THE FIFTH-GRADER SAYS:
Obviously, you want to invest as much as possible where you get the most profit,
so you should be aggressive and invest 30,000,000, pesos in option C).
For the remaining 100,000,000-30,000,000=70,000,000 pesos,
you want to invest as much as possible in B), 
but since they advise to invest  at least 3 more times in A) than in B),
you split that 70,000,000 pesos into four equal parts,
invest 1/4 (17,500,500 pesos) in B),
and the other 3/4 (52,500,000 pesos in A).
You expect to earn
12% of 30,000,000 pesos (3,600,000 pesos) from C),
5% of 17,500,000 pesos (875,000 pesos from B), and
3% of 52,500,000 pesos (1,575,000 pesos from A),
for a total return of 6,050,000 pesos
(6.05% of your 100,000,000 investment),
which is the maximum profit predicted.
End of story.
 
THE MORE IMPRESSIVE EXPECTED GROWN-UP RESPONSE:
You produce a slide presentation with lots of color, music, and inspirational pictures.
You show tables of data with marketing studies' results backing up the projected 12% return for the new startup company.
You present expert opinions backing up the investment constraints advice.
You throw in jargon financial terms,
mention linear programming as an important mathematical tool,
and present the answers to the problem questions,
with all possible mathematical terms and graphs.
Your mesmerized audience congratulates you on your analysis on how to maximize profits.
You get a promotion,
and the fifth grader maximizes the number of chocolate chip cookies that can be swiped from the board room table.