Problem 1 (40 points) H&W company is preparing its aggregate production plan for the first 6 months of 2024. The monthly demand forecasts are given as follows: The company is expected to have 100 workers on the payroll and 150 units in inventory at the end of Month 6. Each worker can produce 10 units. Additional data are given: 1. Production cost $200 per unit 2. Hiring cost $500 per worker 3. Firing cost $3000 per worker 4. Inventory holding cost is $50 per unit per month 5. Shortage cost is $75 per unit per month Follow what we discussed in class. Formulate a linear programming (LP) model that will determine the optimal production plan. Define your variables clearly, write out the constraints that must be satisfied, and write the objective function with explanations