Linear Programming Homework: Max Return with $6M & $5M Budget

In summary, Eva, a senior analyst at 4-Closure Associative, is working on determining the optimal investment policy for her company. With a budget of $6 million for year 1 and $5 million for year 2, Eva must decide how to invest in various projects, including Rauncho, Mondo, Wriggly, Glory, and Upson. Each project can be undertaken up to 100% and any funds not invested can be put into a money market account earning 11% interest. To maximize her funds at the end of year 2, Eva must formulate a linear program with decision variables for each project's investment, as well as a new variable for funds not invested. The objective function will include the
  • #1
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Homework Statement



Eva, senior analyst, is determining the optimal investment policy for her reality company, 4-Closure Associative. She has a budget of $6 million for year 1 and $5 million for year 2, and each project can be undertaken as a fraction, up to 100%. Her investment possibilities, in thousands, include, if invested 100%:

project; investment in year 1; investment in year 2; Return end of year 2
Rauncho; 1400; 1000; 3100
Mondo; 200; 70; 450
Wriggly; 2800; 1600; 5300
Glory; 900; 500; 2100
Upson; 1100; 700; 2400

(i hope it looks clear, it would look clear if you draw a table)
Funds not invested can be put into a money market account paying 11%.
Eva wants to maximise hers funds at the end of year 2.
Formulate a return-maximising Linear program for eva

Homework Equations





The Attempt at a Solution



decision variables:
let x1 be the investment in project Rauncho
x2 be the investment in project Mondo
etc...
x5 be the investment in project Upson

Maximising so:
(MAX) f = 3100x1 + 450x2 + 5300x3 + 2100x4 + 2400x5

subject to the constraints:

1400x1 + 200x2 + 2800x3 + 900x4 + 1100x5 <= 6000000
1000x1 + 70x2 + 1600x3 + 500x4 + 700x5 <= 5000000

Is that correct?
and also i don't know what to do about the part in the question that says:
'each project can be undertaken as a fraction, up to 100%'
and
'Funds not invested can be put into a money market account paying 11%.'

Thank you very much.
 
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  • #2
It's not very important to know what i should do with the part where it says:
'each project can be undertaken as a fraction, up to 100%'
but i really have to know what i ahould do with:
'Funds not invested can be put into a money market account paying 11%.'

i was thinking about it and maybe i have to inclue a new variable in my constraints to be the money not invested but i still don't know how to do this sincei don't know what will be the coefficient of this new variable; i mean will it be 11% of 5 million and 6 million ?

Any help or ideas would be very much appreciated.
Thank you
 
  • #3
I have been working on it and i figured out that we should add a new variable, say x6, where x6 is the money that has not been invested each year.

so this changes the objective function. I am not 100% sure if this is correct but i think the objective function will be something like this:
(MAX) f = 3100x1 + 450x2 + 5300x3 + 2100x4 + 2400x5 + x6(1.11)^2
(i put 1.11 because of the 11% and i put squared because we have two years)
the first constraint will be:
1400x1 + 200x2 + 2800x3 + 900x4 + 1100x5 +x6 = 6000
(since any money left over is x6 and so the total will equal to the total)

but I am not 100% sure how to do the second constraint because we also have to add the money that is left from year one.

Any ideas? please. Thank you.
 

Related to Linear Programming Homework: Max Return with $6M & $5M Budget

1. What is linear programming and how does it relate to budget allocation?

Linear programming is a mathematical technique used to optimize a linear objective function, subject to linear constraints. In the context of budget allocation, it can be used to determine how to allocate funds among different projects or investments in order to maximize a certain outcome, such as return on investment.

2. How do you solve a linear programming problem?

To solve a linear programming problem, you first need to set up the objective function and constraints in a mathematical form. Then, you can use various methods such as the Simplex algorithm or the Interior-Point method to find the optimal solution that maximizes or minimizes the objective function while satisfying all constraints.

3. What are the key components of a linear programming problem?

The key components of a linear programming problem are the decision variables, objective function, and constraints. The decision variables represent the quantities that need to be determined, the objective function is the linear expression that is to be maximized or minimized, and the constraints are the limitations or restrictions on the decision variables.

4. How can linear programming be applied to the given scenario of allocating a $6M and $5M budget?

In the given scenario, linear programming can be applied by setting up the objective function as the return on investment and the constraints as the budget limitations. The decision variables would represent the amounts allocated to different projects or investments, and the solution obtained would be the optimal allocation that maximizes the return within the given budget constraints.

5. Can linear programming handle more complex budget allocation scenarios?

Yes, linear programming can handle more complex budget allocation scenarios with multiple objectives, non-linear constraints, and multiple decision variables. However, as the complexity of the problem increases, the computational effort required to find an optimal solution also increases.

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