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Supply and Demand with Total Profit

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Assuming that a competitive firm has the total cost function:

TC = 1q3 - 40q2 + 710q + 1700

and suppose the price of the firm's output (sold in integer units) is $550 per unit.

Use tables (but not calculus) to find a solution and answer what is the total profit at the optimal output level, with an answer specified as an integer?

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Solution Summary

This solution offers step-wise calculation to show the total profit at optimal output levels, for a firm, given it's total cost function.

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Answer to 584417
Assuming that a competitive firm has the total cost function:

TC = 1q3 - 40q2 + 710q + 1700

and suppose the price of the firm's output (sold in integer units) is $550 per unit.

Use tables (but not calculus) to find a solution and answer what is the total profit at the optimal output level, ...

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Recent Feedback
  • "Thankyou for the feedback. I have a few question though; With the first statistic about cost below... “According to Sigma-Aldrich catalog, cost of 1L octane is AUD $ 392.00, whereas the cost of 1L ethanol is AUD $196.00. Moreover, if ethanol is obtained from sugar industry as a by-product, it may cost even less. Source of oxygen is ambient atmosphere, so it costs nothing. So ethanol is much cheaper than petrol, in fact it is half-priced: AUD $ (392-196) = $ 196.” I didn't think it made sense because the cost of petrol per litre is normally a dollar something or even less than a dollar not a couple of hundred of dollars. For example, a statistic that I found in america was: "U.S. ethanol production costs are about $1.20 per gallon of ethanol, or $1.82 per gallon on a gasoline-equivalent basis." However, I was wondering whether you could find an Australian statistic. Also, you mentioned that H20 is not a greenhouse gas. However, in the combustion equations it is actually carbon dioxide and water vapour which are produced and they are both greenhouse gases. Finally, how do I calculate the energy efficiency of ethanol and petrol? "
  • "Thank you!"
  • "Didnt really answer my questions but gave me a start at least."
  • "Once again this is tremendous help I can't thank you enough for not only working the problem but explaining in detail how and why!! KR"
  • "Awesome thank you so much for the help!!!"
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