Question

Densepack is to plan workforce and production levels for the six-month period January to June. The firm produces a line of disk drives for mainframe computers that are plug compatible with several computers produced by major manufacturers. Forecast demands over the next six months for a particular line of drives produced in the Milpitas, California, plant are 1,280,640,900,1,200,2,000, and 1,400 . There are currently (end of December) 300 workers employed in the Milpitas plant. Ending inventory in December is expected to be 500 units, and the firm would like to have 600 units on hand at the end of June. Cost of hiring workers, cost of firing workers, and cost of holding inventory are as follows:

CH = Cost of hiring one worker =$500,
CF = Cost of firing one worker =$1,000,
CI = Cost of holding one unit of inventory for one month =$80.
​K = Number of aggregate units produced by one worker in one day =0.14653 We assume that there are 20,24,18,26,22, and 15 working days for January to June, respectively.

Answer 1

The question involves labor management, production planning, and economies of scale in response to rising wages in a business setting. Strategic decisions using opportunity cost principles are key to optimizing production processes.

Step-by-step explanation:

The question deals with labor management and production planning in response to rising wages in a firm. In a scenario where the wage has increased to $24 an hour, the firm is incentivized to adopt a plan that requires less labor and more automation. By investing in machinery, workers become more productive due to better equipment. However, this leads to a reduction in the number of workers needed. Determining the optimal workforce and production levels in light of cost considerations such as hiring, firing, and inventory holding is essential for operational efficiency.

For instance, in the case of semiconductor production discussed in Table 33.15, economies of scale become an important factor. These are illustrated by sketching a curve which typically shows declining average costs of production as the quantity produced increases. The question then explores how international trade could enable even a small economy to achieve economies of scale by accessing larger markets and thus producing more units, which drives down average costs and benefits from competition and diversity of products.

Lastly, in the context of Alpine Sports, the firm would choose the plant with the lowest opportunity cost to shift production from skis to snowboards. This is a strategic production decision that maximizes output while minimizing foregone alternatives.