Problem 8-7 Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,100; winter, 8,100; spring, 7,100; summer, 12,100. Inventory at the beginning of fall is 505 units. At the beginning of fall you currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring only if overtime is necessary to prevent stockouts at the end of those quarters. Overtime is not available during the fall. Relevant costs are hiring, $100 for each temp; layoff, $200 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; straight time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. In each quarter, produce to the full output of your regular workforce, even if that results in excess production. In Winter and Spring, use overtime only if needed to meet the production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of reducing the number of temp workers in Summer. (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round up "Number of temp workers, Workers hired and Workers laid off" to the next whole number and all other answers to the nearest whole number.) Fall 10,100 505 9595 Winter 8,100 0 Spring 7,100 0 7100 14200 Summer 12,100 100 11000 12000 19190 24000 14400 14400 14400 22000 14400 7600 15.83 0 Forecast Beginning inventory Production required Production hours required Production hours available Overtime hours Temp workers Temp worker hours available Total hours available Actual production Ending inventory Workers hired Workers laid off 0 9.98 0 0 4790 14400 7600 14400 11000 0 20 9600 14400 12000 14400 7200 7200 0 0 100 0 0 0 0 20 0 0 0 20 Fall 72000 Winter 72000 60800 Spring 72000 Summer 72000 $ $ 0 0 0 0 0 500 0 Straight time Overtime Inventory Backorder Hiring Layoff Total 0 0 29000 0 1000 2000 0 0 0 0 0 400 $ 101000 $ 132800 $ 72500 $ 79000 Annual cost $ 385300