PLEASE GIVE STEP-BY-STEP REASONING AND CLEAR WRITING. PLEASE ANSWER ALL PARTS!

A scheduling problem: A hospital wants to make a weekly night shift (12pm-8am) schedule for its nurses. The demand for nurses for the night shift on day j is an integer dj,j 1,...,7. Every nurse works 5 days in a row on the night shift. The problem is to find the minimal number of nurses the hospital needs to hire. Part A A potential approach A: Let yi be the number of nurses that work on day j. What is the limitation of approach A? Part B Please provide approach B that overcomes the limitation. Part C How could you categorize this Problem 3 among three programmings approaches? (e.g., Linear Programming, Linear Integer Programming, Non Linear Programming)