Finding the min numbers whilst meeting specific conditions

[NVIC1009]

HI there I was wondering if someone can help me. I am working on a project that is incredibly hard to test, therefore we decided to come up with a simplified problem to take the first steps in resolving our problems. My problem is that I can't solve this simple problem using maths in excel so was wondering if someone can help me.

What I am trying to achieve is the smallest $ value minimum investment without breaching any of my set conditions.

I have 2 investments, Investment 1 and Investment 2
Each of these investments have 2 conditions, Bucket A and Bucket B of which they have to contain a value in between the minimum and maximum of these buckets. I am trying to minimize the amount of money invested in each investment whilst meeting the conditions of each bucket.



[TABLE="width: 370"]
<tbody>[TR]
[TD][/TD]
[TD][/TD]
[TD]inv 1
[/TD]
[TD]inv 2
[/TD]
[/TR]
[TR]
[TD]Min. Investment
[/TD]
[TD]$1,000
[/TD]
[TD]x
[/TD]
[TD]y
[/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD][/TD]
[TD]
Min
[/TD]
[TD]$ Value
[/TD]
[TD]Max
[/TD]
[/TR]
[TR]
[TD]Bucket A
[/TD]
[TD]10%
[/TD]
[TD]x
[/TD]
[TD]50%
[/TD]
[/TR]
[TR]
[TD]Bucket B
[/TD]
[TD]40%
[/TD]
[TD]y
[/TD]
[TD]90%
[/TD]
[/TR]
</tbody>[/TABLE]



So based on an overall investment of $1,000 you can see that the minimum investment for Inv 1 is $100 and the maximum investment is $500, similarly for Inv 2 the min. is $400 and the max is $900.

Using a mathematical equation in excel, can anyone please tell me how i can get to $1,000 investment, using the smallest allocation to each investment. Note the investment for Inv1 and Inv2 cannot be below their minimum or above their maximums. Hope this makes sense and someone is able to help me with an excel equation.

Many thanks for your assistance.
Nina