A fuel cell manufacturer can hire union, non-union permanent, or temporary workers. She has a contract to produce at the rate of 2,100 fuel cells per day and aims to achieve this at minimum cost.

- Union Workers:
- Work 7 hours per day.
- Can produce up to 10 fuel cells per hour.
- Wages and benefits cost the company $15.00 and $7.00 per hour, respectively.
- Assured that no more than 80% of their number will be working in non-union permanent positions and no more than 20% in temporary positions.

- Non-union Permanent Workers:
- Work 8 hours per day.
- Can also produce up to 10 fuel cells per hour.
- Wages are the same as union employees, but benefits are worth only $3.00 per hour.

- Temporary Workers:
- Work 6 hours per day.
- Can produce up to 5 fuel cells per hour.
- Earn only $10 per hour.
- Do not receive any benefits.

How many union, non-union permanent, and temporary workers should be hired to minimize the cost to the manufacturer? What is the average cost of producing a fuel cell?

Question

22-04-2025
Business

High School

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A fuel cell manufacturer can hire union, non-union permanent, or temporary workers. She has a contract to produce at the rate of 2,100 fuel cells per day and aims to achieve this at minimum cost.

- Union Workers:
- Work 7 hours per day.
- Can produce up to 10 fuel cells per hour.
- Wages and benefits cost the company $15.00 and $7.00 per hour, respectively.
- Assured that no more than 80% of their number will be working in non-union permanent positions and no more than 20% in temporary positions.

- Non-union Permanent Workers:
- Work 8 hours per day.
- Can also produce up to 10 fuel cells per hour.
- Wages are the same as union employees, but benefits are worth only $3.00 per hour.

- Temporary Workers:
- Work 6 hours per day.
- Can produce up to 5 fuel cells per hour.
- Earn only $10 per hour.
- Do not receive any benefits.

How many union, non-union permanent, and temporary workers should be hired to minimize the cost to the manufacturer? What is the average cost of producing a fuel cell?

Answer :

Final answer:

To minimize the cost, solve a system of equations. Average cost per fuel cell can be found by dividing the total cost by the total number of fuel cells.

Explanation:

To minimize the cost to the manufacturer, the number of union, non-union, and temporary workers that should be hired can be determined by solving a system of equations. Let's denote the number of union workers as U, non-union permanent workers as N, and temporary workers as T. The total number of fuel cells produced per day can be expressed as 7U + 8N + 6T = 2100. The cost can be calculated by multiplying the number of workers by their respective wage rates and adding their benefits. The average cost per fuel cell can be found by dividing the total cost by the total number of fuel cells produced.

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