A Company Can Decide How Many Additional Labor Hours to Acquire

question 106

Essay

A company can decide how many additional labor hours to acquire for a given week.Subcontractor workers will only work a maximum of 20 hours a week.The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C.In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C.Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C.Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C.Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and worker 3 demands a salary of $45/hr.The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost.
(a)Formulate this as a linear programming problem.
(b)Find the optimal solution.

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Definitions:

Paid Parental Leave

A workplace benefit that allows parents to take time off work with pay to care for their new child.

Paternity Leave

Authorized absence from work granted to a father after or shortly before the birth of his child, to support caregiving and bonding.

U.S. Firms

Companies or businesses that are incorporated or operate in the United States, across various industries.

Germany

A country in Central Europe known for its rich history, culture, and significant contributions to science, arts, and philosophy.