Plan production for next year. The demand is spring, 20,026; summer, 10,000; fal
ID: 467280 • Letter: P
Question
Plan production for next year. The demand is spring, 20,026; summer, 10,000; fall, 15,000; winter, 18,000. At the beggining of spring, you have 76 workers and 1,000 units in inventory. The union contract specifies that you may lay off workers only once a year, at the beggining of summer. Also, you may hire new workers only at the of summer to begin regular work in the fall. The number of workers laid off at the beggining of summer and the number hired at the end of summer should result in planned production levels for summer and fall that equal the demand forecasts for summer and fall, respectively. If demand exceeds supply, use overtime in spring only, which means thast backorders could occur in winter. You are given these costs: hiring, $100 per new worker, layoff, $200 per worker laid off; holding $20 per unit-quarter; backorder cost, $8 per unit; straight-time labor, $10 per hour; overtime, $15 per hour. Productivity is 0.5 unit per worker hour, eight hours per day, 50 days per quarter. Find the total cost. /Please I need step by step
Explanation / Answer
Quarter spring summer fall winter Total Demand 20026 10000 15000 18000 Beginning inventory 1000 0 0 0 Production required 19026 10000 15000 18000 Regular workforce 76 50 75 75 Workers Laid off 0 26 0 New Workers Hired 0 0 25 0 Regular production hours (no. of worker *8*50) 30400 20000 30000 30000 Regular production (production hours/0.5) 15200 10000 15000 15000 Shortfall 3826 0 0 3000 Overtime in hours 7652 0 0 0 Overtime production 3826 0 0 0 Total production 19026 10000 15000 15000 Ending inventory 0 0 0 -3000 Inventory cost ($20 per quarter) 0.00 0.00 0.00 0.00 0.00 Back order cost ($ 8 per unit) 0 0 0 24000 24000.00 New Hiring cost ($ 100 per worker) 0 0 2500 0 2500.00 Layoff Cost ($200 per worker) 0 5200 0 0 5200.00 Regular production cost ($ 10 per hour) 304000 200000 300000 300000 1104000.00 Overtime Cost ($ 15 per hour) 114780 0 0 0 114780.00 Total production Cost 418780.00 205200.00 302500.00 324000.00 1250480.00