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MMLU-Pro / 598 / Company A has found that if it offers a guarantee on its transistor radios, more…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Company A has found that if it offers a guarantee on its transistor radios, more will be sold than without the guarantee. In a year, the company expects to sell 100 radios if no guarantee is offered, but if the length of the guarantee is t years then the number sold will be Q = 100 + 5t. It is known that 10% of radios sold will fail each year. The cost of fixing a radio is 1andaprofitof1 and a profit of 2.80 is made on every radio sold. What is the length of the guarantee period t that maximizes profit?
Plain-text mathematical notation (without MathML)
Company A has found that if it offers a guarantee on its transistor radios, more will be sold than without the guarantee. In a year, the company expects to sell 100 radios if no guarantee is offered, but if the length of the guarantee is t years then the number sold will be Q = 100 + 5t. It is known that 10% of radios sold will fail each year. The cost of fixing a radio is 1andaprofitof2.80 is made on every radio sold. What is the length of the guarantee period t that maximizes profit?
Original LaTeX notation
Company A has found that if it offers a guarantee on its transistor radios, more will be sold than without the guarantee. In a year, the company expects to sell 100 radios if no guarantee is offered, but if the length of the guarantee is t years then the number sold will be Q = 100 + 5t. It is known that 10% of radios sold will fail each year. The cost of fixing a radio is $1 and a profit of $2.80 is made on every radio sold. What is the length of the guarantee period t that maximizes profit?

category

business

options

  1. 2 years
  2. 3 years
  3. 6 years
  4. 4 years
  5. 8 years
  6. 10 years
  7. 9 years
  8. 7 years
  9. 1 year
  10. 5 years

src

stemez-Business

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Source and history

upstream_id / Original problem ID
598
task_id
2546a9f5-90e2-5066-9532-a5e399c85a99
task_key
default--test--598
task_revision_id
1
config / split
default / test

Official source

initial import