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.

Q1) A clay potter wants to make and sell bowls and plates. A bowl uses 5 pounds of clay. A plate uses 4 pounds of clay. The potter has 40 pounds of clay and wants to make at least 5 bowls. The profit on a bowl is $32 and the profit on a plate is $34. Write a linear programming formulation for the potter to decide how many bowls and how many plates should the potter make to maximize the profit? (Just write the mathematical formulation)