## linear programming question

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
valkyr
Posts: 2
Joined: Thu Nov 29, 2012 12:45 pm
Contact:

### linear programming question

An investor has up to \$450,000 to invest in two types of investment. Types A pays 6% annually and type B pays 10% annually. To have a well-balanced portfolio, the investor imposes the following conditions. At least one-half of the total portfolios is to be allocated to type A investments and at least one-fourth of the portfolio is to be allocated to type B investments. What is the optimal amount that should be invested in each type of investment? What is the optimal return?

my question is how to get the equations/constraints from this question? i can't really understand how to get it out...

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
Contact:

### Re: linear programming question

my question is how to get the equations/constraints from this question? i can't really understand how to get it out...
You can learn the generalities here.
An investor has up to \$450,000 to invest in two types of investment. Types A pays 6% annually and type B pays 10% annually. To have a well-balanced portfolio, the investor imposes the following conditions. At least one-half of the total portfolios is to be allocated to type A investments and at least one-fourth of the portfolio is to be allocated to type B investments. What is the optimal amount that should be invested in each type of investment? What is the optimal return?
You are asked for the amounts in each investment, so pick variables to stand for the amounts in each investment; maybe "a" and "b". Then start working on constraints. Can you invest negative amounts? What are the minimums they give you? What is the maximum? For the optimization equation, you are asked to maximize the return. What equation represents the return?

valkyr
Posts: 2
Joined: Thu Nov 29, 2012 12:45 pm
Contact:

### Re: linear programming question

umm...i have tried n i got out this equations from the question
let x- types a and y = types b
maximize, 0.06x+0.10y
constraints, x+y<=450,000
y<=x/2

can this be the equation and constraints

nona.m.nona
Posts: 288
Joined: Sun Dec 14, 2008 11:07 pm
Contact:

### Re: linear programming question

let x- types a and y = types b
An alternative might be to use the variables "a" and "b" for types A and B.
maximize, 0.06x+0.10y
As the lesson in the link demonstrated, the optimization equation should be an equation; that is, it should contain an "equals" symbol. You may wish to format as does your book; the equation should be in a form similar to "P = 0.06x + 0.1y".
constraints, x+y<=450,000
It would be wise also to consider the constraint pointed out in the previous reply.
y<=x/2
Where does the exercise state that the amount in the second investment must be less than twice the first investment? Where do you account for the "one-half" and "one-fourth" limits on investments?