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

[sara_87]

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.

 

[sara_87]

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

 

[sara_87]

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.