Here's a simplified resource allocation problem to use as a model in the Interactive Optimizer. Either you can create a file containing these lines and read the file into the Interactive Optimizer by means of this command:

read filename

or you can use the enter command, followed by a name for the problem, followed by these lines:

Minimize
 obj: cost
Subject To
 c1:  - cost + 80 x1 + 60 x2 + 55 x3 + 30 x4 + 25 x5 + 80 x6 + 60 x7 + 35 x8
      + 80 x9 + 55 x10  = 0
 c2:  x1 + x2 + 0.8 x3 + 0.6 x4 + 0.4 x5 >= 2.1
 c3:  x6 + 0.9 x7 + 0.5 x8 >= 1.2
 c4:  x9 + 0.9 x10 >= 0.8
 c5:  0.2 x2 + x3 + 0.5 x4 + 0.5 x5 + 0.2 x7 + 0.5 x8 + x10 - service  = 0
 c6:  x1 + x6 + x9 >= 1
 c7:  x1 + x2 + x3 + x6 + x7 + x9 >= 2
 c8:  x2 + x3 + x4 + x5 <= 0
 c9:  x4 + x5 + x8 <= 1
 c10: x1 + x10 <= 1
Bounds
 service >= 3.2
Binaries
 x1  x2  x3  x4  x5  x6  x7  x8  x9  x10
End

This simple model, for example, might represent a project-staffing problem. In that case, the ten binary variables could represent employees who could be assigned to duty.

The first constraint defines the cost function. In this example, the objective is to minimize the cost of salaries. The next three constraints (c2, c3, c4) represent three nonoverlapping skills that the employees must cover to varying degrees of ability. The fifth constraint represents some additional quality metric (perhaps hard to measure) that most or all of the employees can contribute to. It is called customer service in this example. That variable has a lower bound to make sure of a certain predefined minimum level of 3.2.

The remaining constraints represent various work rules that reflect either policy that must be followed or practical guidance based on experience with this work force. Constraint c6, for example, dictates that at least one person with managerial authority be present. Constraint c7 requires at least two senior personnel be present. Constraint c8 indicates that several people are scheduled for off-site training during this period. Constraint c9 recognizes that three individuals are not productive together. Constraint c10 prevents two employees who are married to each other from working in this group in the same period, since one is a manager.