A university is acquiring mathematical programming software for use in operations research

classes. The four software packages available and the types of optimization algorithms they

provide are indicated by $\text{'}$s in the following table.

$($a$)$ Taking objective function coefficients as the costs of software packages, formulate a set

covering model to acquire a minimum cost collection of software packages providing LP$,$

ILP and NLP capability.

$($b$)$ Taking objective function coefficients as the costs of software packages, formulate a set

partitioning model to acquire minimum cost collection of software packages with exactly

one providing LP$,$ one providing ILP, and one providing NLP$.$