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subject to the constraints
:<math>\sum_{j = 1}^{n}x_{ij}\leq W_{i}\text{ for }i = 1, \ldots, m, \, </math>
:<math>x_{ij}\ge 0\text{ and integer for }i = 1, \ldots, m \text{ and }j = 1, \ldots, n.</math>
Where the variable <math>x_{ij}</math> represents the assignment of as many weapons of type <math>i</math> to target <math>j</math> and <math>q_{ij}</math> is the probability of survival (<math> 1 - p_{ij} </math>). The first constraint requires that the number of weapons of each type assigned does not exceed the number available. The second constraint is the integral constraint.
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