Question

Plan production for the next year. The demand forecast is spring, 20,000; summer, 10,000; fall, 15,000; winter, 18,000. At the beginning of spring, you have 70 workers and 1,000 units in inventory. The union contract specifies that you may lay off workers only once a year, at the beginning of summer. Also, you may hire new workers only at the end of summer to begin regular work in the fall. The number of workers laid off at the beginning 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 that 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, \(10 per hour; over time, \)15 per hour. Productivity is 0.5 units per worker hour, eight hours per day, and 50 days per quarter. Find the total cost.

Short answer

The total cost is $1280, 500.

Step-by-step solution

Production plan for the firm using the given details

The production plan for the firm is given below

The table is shown below: