8.8. Challenges with Integer Linear Programming

Try these first

1. 1.

   What is linear programming?

   Hint

   Think about maximizing profit given some restrictions.

2. 2.

   Why can't we have fractional workers in integer linear programming?

   Hint

   Consider how we apply integers in practical scenarios.

3. 3.

   What is the main challenge of Integer Linear Programming?

   • Limited to fractions
   • Requires integer solutions
   • Easier than LP

   Hint

   Think about real-world applicability of solutions.

4. 4.

   True or False: All solutions from linear programming can be used directly for integer programming.

   • True
   • False

   Hint

   Consider the nature of integer requirements.

5. 5.

   A factory needs to optimize its production over 12 months, encountering fluctuating demand from 500 to 800 units per month. Given the costs associated with hiring, firing, and storage, formulate a linear program that ensures all solutions yield integer workers needed for production.

   Hint

   Think about how rounding may affect your labor costs.

6. 6.

   A local pizza shop needs to analyze its staffing based on varying customer demand. Analyze how ILP can provide insights while preventing fractional staffing solutions. What might the implications be on staffing costs?

   Hint

   Reflect on staffing decisions based on integer constraints and potential impacts.