The U of A is in the process of forming a committee to handle students' grievances. The administration wants the committee to include at least one female, one male, one student, one administrator, and one faculty member. Ten individuals (identified, for simplicity, by the letters a to j) have been nominated. The mix of these individuals in the different categories is given as follows:

CategoryIndividuals

Females........................... Q, b, c, d, e

Males................................ f, g, h, i, j

Students................................ a, b, e,j

Administrators............................. e,f

Faculty................................d, g, h, j

The U of A wants to form the smallest committee with representation from each of the five categories. Formulate the problem as an ILP and find the optimum solution.