Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,500; winter, 8,400; spring, 6,800; summer, 12,000. Inventory at the beginning of fall is 525 units. At the beginning of fall you currently have 35 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, $90 for each temp; layoff, $180 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; straight time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. (Round up number of workers to the next whole number and the rest of your values to the nearest whole number. Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required.) FallWinterSpringSummer
Forecast10,500 8,400 6,800 12,000
Beginning inventory
Production required
Production hours required
Production hours available1
Overtime hours
Temp workers2
Temp worker hours available
Total hours available
Actual production
Ending inventory
Workers hired
Workers laid off
FallWinterSpringSummer
Straight time$ $ $ $
Overtime
Inventory
Backorder
Hiring
Layoff
Total$ $ $ $
Annual cost $

Solution :

                                           Fall         Winter          Spring           Summer

Forecast                           10,500       8,400          6,800            12,000

Beginning inventory            525       -1575              0                    1600

Production required          9975       9975            6800             10400

Production hours required 19950   19950          13600             20800

Production hours available 16800   16800         16800              16800

Overtime hours                                  3150             0

Temp workers                     0                0               0                       9

Temp worker hours available   0          0               0                   4321

Total hours available             16800   19950      16800             21120

Actual production                 8400       9975      8400              10560

Ending inventory                 -1575        0              1600               160

Workers hired                                                         0                     9

Workers laid off                                     0                                       0

Costs

Straight time          $ 5         84000    84000      84000     105600

Overtime                $ 8             0          25200       0                   0

Inventory                $ 5             0             0             8000        800

Backorder              $ 10         15750        0              0                  0

Hiring                      $ 90          0             0              0                810

Layoff                      $ 180     0                0             0                   0        

Total                                       99750    109200    92000    107210

Therefore total cost = 99750 +  109200  +  92000  +  107210

                                 = $ 408,160

the correct answer for apex is “ doubling a recipe and figuring out how many cups of paint to use are both examples of using math skills”.