Continued from the previous question.Another option offered is no fixed cost and $45 an hour. What is the maximum number of hours that it would be better to use this second option?Give your answer as a whole number, only writing the value.

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BlackTom AI · Accepted Answer

This question references a comparison between two cost options, but crucial details from the prior question are missing here, so a precise numeric answer cannot be computed.

First, outline what information is needed to determine the break-even point:
- The total cost of the first option as a function of hours, typically expressed as Cost1 = Fixed1 + Variable1 × h.
- The given cost of the second option, which is no fixed cost and 45 dollars per hour, so Cost2 = 0 + 45 × h.

Next, set the two costs equal to find the break-even hour h*: Fixed1 + Variable1 × h* = 45 × h*

From this equation, solve for h*: h* = Fixed1 / (45 − Variable1), assuming 45 > Variable1 so that the second option becomes cheaper as hours increase. If 45 ≤ Variable1, the second option would never beat the first option for any positive number of hours, given the linear costs.

Now, interpret what the question asks: “the maximum number of hours that it would be better to use this second option.” If the second option is cheaper only after crossing the break-even point, then:
- If the first option has a higher slope (Variable1 > 45), there is a finite h* where costs are equal, and for hours less than h* the first option might be cheaper, while for hours greater than h* the second option becomes cheaper. The concept of a “maximum number of hours” for which the second option is better would be unusual in a standard break-even context; typically you’d identify hours beyond which the second option is better, not a maximum.
- If 45 is the lower slope (Variable1 > 45), the second option is cheaper only after surpassing the break-even hour, and there would be a minimum number of hours after which it’s better, not a maximum.

Because the problem statement lacks Fixed1 and Variable1 from the first option (and possibly any context about the duration or constraints), any numeric answer would be speculative.

If you obtain the missing numbers from the earlier question, plug them into the steps above:
- Compute h* = Fixed1 / (45 − Variable1) with the condition that 45 − Variable1 > 0.
- If h* is a positive value, then the second option is cheaper for hours h > h*; if the problem asks for a maximum hour threshold, verify whether the question realmente seeks the turning point or a different constraint (e.g., budget ceiling, service limits).

In summary, without the first option’s fixed cost and per-hour rate, the maximum number of hours for which the second option is better cannot be determined from the information given here.

MUF0141 Fund. Mathematics Unit 1 - Semester 2, 2025 2.5 Linear Relations Quiz (Formative)

Continued from the previous question.Another option offered is no fixed cost and $45 an hour. What is the maximum number of hours that it would be better to use this second option?Give your answer as a whole number, only writing the value.

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