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.

Q4) Juan makes two types of wood clocks to sell at local stores. It takes him 2 hours to assemble a pine clock, which requires 1 oz of varnish. It takes 2 hours to assemble an oak clock, which takes 4 oz. of varnish. Juan has 16 oz. of varnish in stock and can work 20 hours. He makes $3 profit on each pine clock and $4 on each oak clock. Write a linear programming formulation which decided how many of each type should he make to maximize his profits?