Quadratically constrained MIQP with julia and gurobi

Question

This is an attempt to answer the following question: https://matheducators.stackexchange.com/questions/11757/small-data-sets-with-integral-sample-standard-deviations

So

Answer 1

A math programming solver like Gurobi Optimizer cannot solve models with quadratic equality constraints. Here are the types of constraints that Gurobi Optimizer can solve. To solve your model using Gurobi Optimizer, you must transform your constraints into one of these forms, such as quadratic inequality constraints.