text: # The weekly cost (C) of growing and selling x acres of flowers is approximated by C = 0.2x^2-12x + 240. How many acres of flowers would minimize these costs?
  
  Apr 8, 2018
  
  $C \left(x\right) = 0.2 {x}^{2} - 12 x + 240$
  
  $C ' \left(x\right) = 0.4 x - 12$
  
  Equating this to 0,
  
  $\implies 0.4 x - 12 = 0$
  
  $\implies 0.4 x = 12$
  
  $\implies x = 30$
  
  Again, taking derivative of $C ' \left(x\right) = 0.4 x - 12$
  
  $C ' ' \left(x\right) = 0.4$
  
  $C ' ' \left(x\right) > 0$
  
  Hence, $C \left(x\right) = 0.2 {x}^{2} - 12 x + 240$ is minimised at $x = 30$.
  
  30 acres of flowers would minimize these costs :)
explanation: The document contains a math question and a detailed answer to the question. The question asks how many acres of flowers would minimize the cost, and the answer provides a step-by-step solution to find that 30 acres of flowers would minimize the costs.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # The weekly cost (C) of growing and selling x acres of flowers is approximated by C = 0.2x^2-12x + 240. How many acres of flowers would minimize these costs?
  
  Apr 8, 2018
  
  $C \left(x\right) = 0.2 {x}^{2} - 12 x + 240$
  
  $C ' \left(x\right) = 0.4 x - 12$
  
  Equating this to 0,
  
  $\implies 0.4 x - 12 = 0$
  
  $\implies 0.4 x = 12$
  
  $\implies x = 30$
  
  Again, taking derivative of $C ' \left(x\right) = 0.4 x - 12$
  
  $C ' ' \left(x\right) = 0.4$
  
  $C ' ' \left(x\right) > 0$
  
  Hence, $C \left(x\right) = 0.2 {x}^{2} - 12 x + 240$ is minimised at $x = 30$.
  
  30 acres of flowers would minimize these costs :)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed answer to the question. The question asks how many acres of flowers would minimize the cost, and the answer provides a step-by-step solution to find that 30 acres of flowers would minimize the costs.
  
  Label: question-and-answer