Final answer:
The student's question pertains to a cost function, c(x), used in economics to determine the cost of manufacturing based on production output. If the workers' wages are adjusted, like the union-negotiated $20 per hour, it might influence the total cost and the decision-making process regarding labor and machine use, highlighting the balance between cost efficiency and consumer relations.
Step-by-step explanation:
The concept of c(x), which represents the cost of manufacturing x bicycles, is an example of a cost function used in economics and mathematics. The cost function provides information on how total production costs change with differing levels of output. In this context, the keyword manufacturing cost refers to the unit cost, which is $200 per bicycle as mentioned.
If a union instigates a new wage of $20 per hour, then the cost function might change depending on the labor hours and the number of machines. This leads to an interesting situation, noted in the information provided, where the firm's costs might remain unchanged whether it opts for more labor and fewer machines or vice versa. However, the business factor of worker-consumer relationship, reflected in the idea that 'machines don't buy products,' could influence the firm's decision.
An example of a specific cost function is given when considering a word processing job with a fixed cost of $31.50 and a variable component that depends on the number of hours, x, required to complete the job. Thus the total cost, y, is the sum of the fixed cost and $32 times the number of hours worked: y = 31.50 + 32x.
Similarly, if widget workers receive $10 per hour, the total cost to produce widgets can be found by multiplying the number of hours worked by the wages per hour.