Question: If a linear programming problem has an objective function to be maximized involving 4 controllable variables and 6 linearly independent constraints, all of which are of the form of " \(\le \) " with a linear combination of the 4 controllable variables on the left and a numeric constant (perhaps with units of measurement, perhaps not) on the right:

1. How many slack variables are there when the problem is expressed in standard form?
2. How many surplus variables are there when the problem is expressed in standard form?
3. How many basis vectors are needed to constitute a basis set for this problem?
4. What simple test can be done to determine whether the feasible region is empty versus nonempty?

Bonus: What is the minimum number of binding constraints? What is the maximum number of binding constraints? Explain your answers.

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