a$)$ Formulate this problem as an integer program.

b$)$ Solve the linear programming relaxation of this problem using any method. What is the cost and what is the schedule and shifts of the LP relaxation?

c$)$ Is the solution obtained under b$)$ optimal for the original problem?

d$)$ If the solution is not optimal, solve two additional versions of the LP by adding a constraint to each LP$,$ rounding up and rounding down the answer of b$.$ Is any one of the new LP solutions optimal?

Please help me with all parts and show work as well!