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Mr. David manufacturers and sells a single product a fixed price in a niche market. The selling price of each unit is Rs. $30.$ On the other hand, the cost, in rupees, of producing x units is $240+bx+cx^2$ where $b$ and $c$ are some constants. Mr. David noticed that doubling the daily production from $40$ to $60$ units results in an increases the daily production cost by $66.66\%.$ However, an increase in daily production from $40-60$ units results in an increase of only $50\%$ in the daily production cost, Assume that demand is unlimited and that Mr. David can sell as much he can produce. His objective is to maximize the profit.

What is the maximum daily profit, in rupees, that Mr.David can realize from his business?

  1. $620$
  2. $920$
  3. $840$
  4. $760$
  5. cannot be determined
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