linear programming question

[valkyr]

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...
please help me out.....thank you

[maggiemagnet]

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?

If you get stuck, please reply showing your answers for my questions so far. Thanks!

[valkyr]

thank you for replying
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]

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?