3. [20 points] [Mathematical Programming Formulation] Demands in the next four months for a product are given as follows: 40, 20, 60, 15. However, the company making this product has a limited production capacity of 50 units in any month. The company has to set up the production line before any manufacturing activity can happen. The fixed cost of the setup is $2,000 in each month that the production line is set up. In addition, the manufacturing cost is $200 per product. Products can be held in inventory for $100 per unit per month. We would like to formulate this problem as an integer program. (a) (4 points] Define the decision variables with all necessary information. (b) [5 points] Write the objective and objective function mathematically. (c) (11 points) Write the constraints mathematically