Write the mathematical formulation for the following problems. Clearly state the variables (eq. x, y, z) and the meaning of the variables used by you in the formulation. Write the objective function and the constraints for the linear programming problem.

No Need to find the optimal solutions, just write the formulation.

Q5) At a university, Professor Symons wishes to employ two people, John and Mary, to grade papers for his classes. John is a graduate student and can grade 20 papers per hour; John earns $15 per hour for grading papers. Mary is a post-doctoral associate and can grade 30 papers per hour; Mary earns $25 per hour for grading papers. Each must be employed at least one hour a week to justify their employment.

If Prof. Symons has at least 110 papers to be graded each week, write a linear programming formulation to compute how many hours per week should he employ each person to minimize the cost?