Plan production for a four-month period: February through May. For February and March, you should produce to exact demand forecast. For April and May, you should use overtime and inventory with a stable workforce; stable means that the number of workers needed for March will be held constant through May. However, government constraints put a maximum of 5,000 hours of overtime labor per month in April and May (zero overtime in February and March). If demand exceeds supply, then backorders occur. There are 100 workers on January 31. You are given the following demand forecast: February, 75,000; March 70,000; April 80,000; May, 60,000. Productivity is four units per worker hour, eight hours per day, 20 days per month. Assume zero inventory on February 1. Costs are hiring, $50 per new worker; layoff, $75 per worker laid off; inventory holding, $10 per unit-month; straight-time labor, $10 per hour; overtime, $15 per hour; backorder, $20 per unit a. Find the total cost of this plan? I: Relevant information includes: Backorder cost per unit Holding cost per unit Number of Workers at the end of January Hiring cost per worker Layoff cost Er worker [:1 Production time (hours)_per unit Straight time labor cost per hour Overtime labor cost per hour Working time (hrs/day) Work days per month Beginning inventory Aggregate Production Planning Requirements Time Period February March April Forecast Beginning Inventory Production Required (Forecast - Beginning inventory) Production hours required (# units * Production Time per unit) Regular workforce Regular production (Production hrs available] Labor hrs required per unit) Overtime hours Overtime production Total production (Production hours required I Production time per unit) Ending Inventory (Beginning inventory + Actual production - Demand forecast) Workers hired Workers laid off Straight Time (Production hrs available x Straight time labor cost) Overtime Inventory cost Backorder cost Hiring cost Layoff cost Total costs Total Cost