Develop a production plan and calculate the annual cost for a firm whose demand forecast is: fall, 10,100; winter, 8,400; spring, 7,000; summer, 12,100. Inventory at the beginning of fall is 505 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 if overtime is necessary to prevent stock-outs 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; regular 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.

Check the explanation

Explanation:

                                                    Fall  Winter  Spring  Summer

Forecast                                     10,100  8,400  7,000  12,100

Beginning Inventory                   505  -1,195  0          1,400

Production required                 9,595  9,595  7,000  10,700

Production hours required        19,190  19,190  14,000  21,400

Production hours available1  16,800  16,800  16,800  16,800

Overtime hours                              0      2,390     0           0

Temp workers2                              0         0          0           10

Temp worker hours available      0            0          0          4,800

Total hours available                 16,800  19,190  16,800  21,600

Actual production                        8,400  9,595  8,400  10,800

Ending inventory                           -1,195     0        1,400  100

Workers hired                                 0           0            0            10

Workers laid off                                0          0            0            10

                                       Fall  Winter             Spring  Summer

Straight Time         $84,000  $84,000  $84,000  $108,000

Overtime                            0  $19,120                 $0             $0

Inventory                          $0        $0             $7,000            $500

Backorder                   $11,950    $0                    $0               $0

Hiring                                $0        $0                 $0            $900

Layoff                                $0       $0                  $0            $1,800

Total                           $95,950  $103,120     $91,000  $111,200

Annual Cost                                                                $401,270

kindly check the calculation in the image below.