22. (15 points) The company wants to determine the production plan for the next 6 months. At the beginning of the first month, the company have 5,000 products in the inventory. The demands and production costs per unit for each month are shown in the table below. All the demands must be satisfied for each month. The holding cost per unit at the end of each month is 5% of the production cost per unit for that month. The setup cost for each month is $10,000 (fixed cost). The production capacity for each month is 50,000 and inventory capacity is 20,000. 4 6 Month 1 2 5 Demand 10,000 15,000 30,000 35,000 25,000 10,000 Production Cost 12.50 12.55 12.70 12.80 12.85 12.95 Based on information above, formulate the mathematical model to find the optimal production plan for the next 6 months to minimize the total cost (modeling only, no need to solve). Specifically: (a) (4 points) Define the decision variables and supporting variables (if needed). (b) (3 points) Determine the objective function. (c) (8 points) Determine the constraints. Note: Notations and symbols can be defined to simplify your model