Long and Tough Problem - Need Possible Solutions

[MarrowGenx]

First, I would like to thank you for taking the time to read this. I appreciate any and all feedback/solutions you can offer.

I have the following objects:

Objective
Activity
Obj-Act Relationship

Here is how my db is working:

Objectives are possible problems that need a solution. Activities are solutions to possible problems. An Objective can have one or more possible Activities that meet it. An Activity can meet multiple Objectives. This is the reason for the Obj-Act Relationship. To top that off, Activities can partially (numerical value of 1) or fully (numerical value of 2). So you can have two Activities that are required to meet the Objective (i.e. to answer an Objective, you must have 2 points, either two partially or one fully). The partially or fully meeting value is held in the Obj-Act Relationship table (because one activity may fully meet one Objective and partially meet another).

Now my problem:

I need to find the best possible path(s) that will allow me to complete the fewest number of Activities and meet (value of 2) all Objectives.

If this is not clear, please reply back and I will give examples to explain. Once again, I appreciate any and all help that you can provide me with.

Marrow

 

[Geo45]

Can you give a small example of what problem is entered and what sort of thing is entered as a solution.

 

[MarrowGenx]

Here is a possible scenario:

Objective - Activity - Partially or Fully Met
Obj1 - Act1 - Fully
Obj1 - Act2 - Fully
Obj2 - Act3 - Partially
Obj2 - Act1 - Fully
Obj2 - Act4 - Partially
Obj3 - Act5 - Fully
Obj4 - Act6 - Partially
Obj4 - Act7 - Partially
Obj5 - Act2 - Fully
Obj6 - Act1 - Fully

I want to find the least number of Activities that I have to perform to complete all the Objectives (completed is denoted by either one Fully Met or two Partially Met).

Solution:

Obj1 - Act1
Obj2 - Act1 or Act 2
Obj3 - Act5
Obj4 - Act6 and Act7
Obj5 - Act2
Obj6 - Act1

The actual number of Activities and Objectives and relationships are much higher in number than the example above. Thanks for the reply Geo45.