Question: A manufacturer produces bowls and mugs. The manufacturer can get $40 profit for each bowl and $50 for each mug. However, there are several resource constraints for the manufacturer. Each bowl need 2 labor hours and 40 pounds of clay and each mug needs 1 labor hour and 30 pounds of clay, while there are only 52 labor hours and 150 pounds of clays available everyday. The manager's question is how many units of mugs and bowls he should produce so that he can get maximum profit. Please formulate this question using linear programming technique (write the equations representing this information). You are not asked to solve the questions with optical numerical solution.