$1.$ LP model formulation $(30$ pts$)$

a$.(10$ pts$)$ Define the decision variables, objective, and constraints for this LP problem.

b$.(10$ pts$)$ Write down the LP objective function in terms of the decision variables $($i$.$e$.,$ in a mathematical expression$)$

c$.(10$ pts$)$ Write out the constraints in terms of the decision variables $($i$.$e$.,$ in mathematical expressions$)$