Problem 1. (Resource Planning-AggPlan. Total 15 pts,) Given the next 6 months aggregated demand forecast and other related information from the following 4 tables. Table 1. next 6 months aggregated demand forecast Table 2. Types of available productions and costs to produce each product Table 3. The inventory cost for one product per month, and the Backlog cost for each product that needs to be backlogged. Table 4. Inventory of products that is available at the beginning of January. Table 1. Demand forecast Table 2. Types of available production and Other Related Information Month Project Demand (unit) Available Production Regular Overtime Subcontract Jan 250 Monthly Capacity (in units) 200 40 150 Feb 200 Operation Cost (per unit) $100 $130 $140 Mar 200 Apr 650 Table 3. Inventory and Backlog Costs May 550 Inventory Backorder Jun 100 Cost (per Month) $10 $15 Total Table 4. Inventory Relatd Information (in unit) Given Beginning 50 Required End of June 100 To do the followings a) i) develop a Feasible Aggregate Plan for the coming six-month demand forecasted. A Feasible Aggregate Plan is a plan that meets the end-of-June inventory requirement. ii) For the aggregate plan you have developed in a-i), calculate the 6-month costs of Regular production; Overtime production; subcontract; plus costs that occurred due to Inventory and Backlog, Finally. the Total 6- month costs of your Aggregate Plan. b) Discuss whether or not the plan you developed in a) is the Best. Explain why? If it is not the Best, use a systematic approach to revise your plan so that the total costs are Minimized, or at least better. Please explain why your revised plan will be better. Varify your result by recalculate the total costs.