Instructions: This assignment has two questions. The full credits are 20. Problem 1 (10 points): Tom opens a plant. The plant can produce two products: a chair and a table. Each chair can earn $6, and each table can earn $8. Each chair costs 2 hours of labor and 4 pounds of wood to make, and each table costs 3 hours and 5 pounds of wood to make. The plant has 20 hours of labor and 40 pounds of wood available. Tom wants to maximize his profits by producing these two types of products. Please formulate this problem using linear programing. (1) Please define the decision variables in this problem. (2 points). (2) Please list the objective function. (3 points) (3) Please list all constraints. (5 points) Problem 2 (10 points) A company is producing two types of products: bowl and mug. Each bowl needs to have 2 hours of labor, and 4 pounds of clay, which can earn 100 dollars per unit. For each mug, it needs to have 3 hours of labor, and 1 pounds of clay, which can earn 20 dollars per unit. The total number of available labor is 80 hours, and the total number of available clay is 100 pounds. Please use EXCEL SOLVER to find the optimal solutions and the optimal value of the objective function to maximize the earnings. That is, (a) What is the optimal number of bowls to produce? (3 points) (b) What is the optimal number of mugs to produce? (3 points) (c) What is the optimal value of the objective function? (4 points)