Suppose a company needs to determine order quantities for the rest of this fiscal year from October 2022 to June 2023. The company determines whether it should make an order in each month to meet demands. If the company decides to make an order in a month, the company also determines how many units of the product it will order. The monthly demands (in units) estimated for October 2022 to June 2023 are 1000, 2000, 1500, 800, 2400, 2000, 1750, 2800, and 900, respectively. The order costs (in dollars) for October 2022 to June 2023 are 2200, 1150, 2010, 2580, 2140, 2700, 2950, 1910, and 2760, respectively. For example, if the company makes an order in February 2023, the order cost is $2140. The inventory costs per unit per month (in dollars) for October 2022 to June 2023 are 1, 3, 3, 1, 1, 1, 4, 2, and 4, respectively. The company would like to minimize the total cost for the rest of the fiscal year. Stockout or backorder is not allowed. (a) What are decision variables? Please clearly indicate what each decision variable represents. (b) What is the objective function? Please write the objective function using the decision variables identified in part (a). (c) What are the constraints? Please write down each constraint using the decision variables identified in part (a). Please also indicate the purpose of each constraint. (d) What is the type of the mathematical model based on the answers to parts (a), (b), and (c)? In the class, we have discussed LP, ILP, NLP, and INLP.